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Full text of "Mind's Eye: A Liberal Arts Journal Spring 2002"

Spring 2002 

Mind's Eye 

A Liberal Arts Journal 
Massachusetts College of Liberal Arts 




Meditations on Opinion 

By Joe Mazur 

Poetry 

By Sara Littlecrow-Russell 

Giotto's Arena Chapel Frescoes and Religious Theater in His Time 

By Charles Parkhurst 

Water out of a Woodland Spring 

Book Review by Tony Gengarelfy 

Intellectual Fads 

Book Review by Meera Tamaya 

$7.50 



Mind's Eye 

A Liberal Arts Journal 



SPRING 2002 



Massachusetts College of Liberal Arts 



Editorial Board 

Tony Gengarelly, Managing Editor 
Robert Bence 
Bob Bishoff 
Harold Brotzman 
Surni Colligan 
Abbot Cutler 
Steve Green 
Bill Montgomery 
Leon Peters 
Meera Tamaya 
Arlene Bouras, Copy Editor 

Advisory Board 

James MacGregor Burns, Professor of history and political science. 
Universty of Maryland 
Stephen Fix, Professor of English, Williams College 
Thomas Green, Professor of law and history. University of Michigan 
Mary Huber, Carnegie Foundation scholar 
Lea Newman, Professor of English emerita, Massachusetts College of Liberal Arts 
Joseph Thompson, Director of MASS MoCA 

© 2002 The Mind's Eye 
ISSN 1098-0512 

The Mind's Eye. a journal of scholarly and creative work, is published twice 
annually by Massachusetts College ol Liberal Arts. While emphasizing articles 
of scholarly merit. The Mind's Eye focuses on a general communication of ideas 
of interest to a liberal arts college, We welcome expository essays, including 
reviews, as well as fiction, poetry and art. Please refer to the inside back cover 
for a list of writer's guidelines. 

A yearly subscription to The Mind's Eye is $1 5. Send check or money order 
to The Mind's Eye, CIO Tony Gengarelly, Massachusetts College of Liberal Arts, 
375 Church Street, North Adams, MA 01247. 

Massachusetts College of Liberal Arts 
375 Church Street 
North Adams, MA 01247-4100 
Visit our Web site: www.mcla.mass.edu/academics/mindseyexxx 



Mind's Eye 

SPRING 2002 



Editor's File 4 

Meditations on Opinion 

By Joe Mazur 5 

Poetry 

By Sara Littlecrow-Russell 34 

Giotto's Arena Chapel Frescoes and 
Religious Theater in His Time 

By Charles Parkhurst 38 

Water out of a Woodland Spring 

Bouk Review by Tony Gengareliy 55 

Intellectual Fads 

Book Review by Meera Tamaya 61 

Contributors 64 



On the cover; 
Giotto, Joachim 's Vision, c. 1 302-05 



Editor's File 




his is our fifth anniversary issue. To heip us celebrate, we are pleased 
to announce the addition of an Advisory Board, a s well as the inclusion 
of two extraordinary articles from outside contributors. 



In accordance with our newly expanded mission, we arc delighted to 
welcome a group of distinguished professionals, who will compose the Advi- 
sory Board and assist the Editorial Board in its efforts to promote and fund 
The Mind's Eye: Pulitzer Prize-winning historian James MacGregor Burns, 
Carnegie scholar Mary Huber, Professor of English Stephen Fix, MASS MoCA 
Director Joseph Thompson, Professor of Law and History Thomas Green and 
Professor of English emerita Lea Newman. Professor Burns has been a stal- 
wart supporter of the journal's efforts from the outset, and he brings to our 
mission considerable experience with publishing, as well as a broad range of 
knowledge. Mary Huber has also been a good friend to the journal and pro- 
vides a touchstone in a different branch of the academic world. Stephen Fix is 
another longtime friend whose efforts on the MCLA Board of Trustees helped 
launch the journal in 1997. Joseph Thompson, director of one of the world's 
most innovative museums, adds his impressive administrative skills. Thomas 
Green, as editor and scholar, supplies much appreciated expertise as the jour- 
nal looks to a national audience. Lea Newman, an MCLA star in the academic 
firmament, has been a consistent contributor to and inspiration for our efforts. 
Once again, it is our pleasure to welcome these outstanding people to our ranks 
and to begin working with them as the journal continues its evolution. 

This issue features the work of two outstanding scholars. Joe Mazur's en- 
gaging piece, "Meditations on Opinion," is part of a larger work he is currently 
writing. A professor of mathematics at Marlboro College, Joe has published 
widely in his field and is now engaged in a more artistic and philosophical 
reflection on the nature of mathematical truths and related questions. Charles 
Pa rkhuist's long and distinguished ca reer has taken him many places as a scholar 
and a museum administrator. He honors us here with the publication of one of 
his most memorable lectures and academic studies concerning the work of the 
14th-century master artist Giotto. We are also very fortunate to feature the 
poetry of Sara Littlecrow-Russell. Her insights, drawn from the two cultures in 
which she is simultaneously living, are riveting as well as enlightening. Finally, 
the issue is rounded off with two reviews by Mind's Eye editors. The first, by 
Tony Gengarelly, highlights an extraordinary anthology of essays on the work 
of John Fowles, The second, by Meera Tamaya, provides a humorous glance at 
the world of academia. 

We also wish to acknowledge the efforts of those who have helped and 
continue to help nurture the journal on its successful journey; President 
Thomas Aceto. Vice President of Academic Affairs John Frazee, the Board of 
Trustees, the MCLA Development Office, our copy editor, Atlene Bouras, and 
members of The Mind's Eye Editorial Board, noting especially the efforts of lay- 
out and graphics designer Leon Peters. 

4 The Mind's Eye 



Meditations on Opinion 

BY JOE MAZUR 



Before mathematicians consciously process proofs, they unconsciously 
know something is true from what they see and hear, from instinc- 
tual feelings and from rich caches of established beliefs. Those caches 
may include what they see in symbols and pictures, what they feel 
from an unconscious sense of logic and what conflicts with estab- 
lished physical and nonphysical experience. It may surprise readers 
to learn that mathematicians communicate by proofs that omit logi- 
cal detail and think of the impossible as well as the possible. 

"Just the place for a Snark!" the Bellman cried. 

As he landed his crew with care; 
Supporting each man on the top of the tide 

By a finger entwined in his hair, 

"Just the place for a Snark! I have said it twice: 
That alone should encourage the crew. 

Just the place for a Snark! f have said it thrice: 
What I tell you three times is true." 

—Lewis Carroll, "The Hunting of the Snark" 



On a drizzly October afternoon in 1886, Camille Jordan 
entered a small building behind the Pantheon in Paris to 
deliver a lecture to his mathematics class at I'Ecole 
Polytechnique. 1 He had just returned trom a circuitous walk to and 
from the Cafe Luxembourg several blocks away to retrieve an um- 
brella that he had left behind. Such short walks to or from his favorite 
cafe often inspired ciever ideas to help streamline his work or lectures; 
this time his idea was magnificent. He entered a small mahogany- 



The Mind's Eye 5 



Joe Mazur 



paneled classroom through a door reserved for professors and faced 
3 1 students seated in a steep incline of rows. He had taught his fa- 
mous class many times before; but on that particular afternoon, en- 
couraged by his latest idea, he confidently said something that had an 
unexpected consequence. He intended to prove a theorem by means 
of a statement that, he had always thought to be obviously true, so he 
casually relayed it to the class. A vigilant student, seated in the last 
row, politely interrupted the great professor to ask for more evidence 
or a proof of what was claimed to be "obvious." Professor Jordan 
scratched his head, stroked his beard and rapidly blinked his eyes as 
he nervously removed his wire-rimmed glasses from one ear at a time 
and thought about how he would convince the class that the simple 
statement he had made was, indeed, true. After pondering the state- 
ment more carefully for several minutes without saying a word, he 
concluded that perhaps it was not so obvious. 

As the hour progressed, the professor's simple statement fell from 
the obvious into an abyss of vexing uncertainty. The course turned 
from its usual syllabus to the professor's not-so-obviously-true state- 
ment, which turned more and more elusive at every class meeting. 
Jordan spent the year routinely working each day at the Cafe Luxem- 
bourg, consuming coffee and a large number of croissants on which 
he would spread spoonfuls of peach jam, trying to prove the truth of 
his statement. By the following June, he had completed the proof and 
written it in several hundred pages of notes that were published 11 
years later in a 109-page compendium to a three-volume text of his 
lectures. The simple and obvious statement that Professor Jordan ca- 
sually made in October of 1886 was, indeed, true. At least it was true 
for the time being. The story does not end here; we will have more to 
say about this later. 

We often hold opinions without knowing why, and presume them 
to be true without having definite proof. But proper proof is a process 
that can either change an opinion or stiffen it into unyielding persua- 
sion. At some unnoticeable point in that process, we start to subcon- 
sciously "feel" truth. While a mathematician learns a proof of a 
theorem, subconscious links are slowly formed between what is being 
proved and an intricate, gigantic web of connections to old, estab- 
lished theorems in his or her cache. Professor Jordan's feeling of truth 
for his statement came long before he had any argument to back it up. 

6 The Mind's Eye 



Joe Mazur 



Huw could he have known that the statement was true nine months 
before he was able to make any conclusively deductive arguments? 
Mathematics enjoys the honorable distinction of being free from judg- 
ment, yet even mathematicians often form strong opinions without 
bothering to link them to the usual deductive network of known math- 
ematics. Camille Jordan struggled with the forces that separate un- 
substantiated opinion from proven fact. Driven by his unconscious 
instinct to substantiate his hunch, he had to find a way to prove he 
was right; he started by confusing his initial opinion with a "feeling" 
of truth and tried to communicate that feeling to others. 

The simple statement that Camille Jordan had innocently thought 
was so obvious when he first used it in his class is the following: "Ev- 
ery continuous curve that begins and ends at the same point without 
crossing itself divides the plane in two." Surely, a circle is a specific 
example of the kind of curve Jordan had in mind; it fits the descrip- 
tion as a curve that separates the plane into two regions, those points 
that are inside the circle and those that are outside. If we think about 
it for a few minutes and perhaps doodle with pencil and paper, we are 
likely to agree that it is obvious that every continuous curve that be- 
gins and ends at the same point without crossing itself divides the 
plane in two. But mathematicians are very suspicious of claims of the 
"obvious" without some hard evidence of "truth," even though, more 
often than not, their intuition turns out to be right. Mathematicians 
seem to sense mathematical truth! They may use the word "obvious" 
to communicate a strong belief that a formal proof can be found lurk- 
ing behind a heuristic argument; after ail, the whole notion of proof in 
mathematics has never been clearly defined. They can make true state- 
ments long before formal proofs are found! Perhaps some rough, un- 
conscious proof processing makes certain things feel obvious. So, in 
presenting a proof, the mathematician comfortably assumes that his 
or her audience will be convinced, despite the omission of logical de- 
tail. But occasionally the omission backfires. 

Nobody believes that all triangles are isosceles, 2 yet Lewis Carroll 
designed a very convincing argument suggesting that they are. His 
argument is hard to refute; yet when it is given, our opinion is firm: 
We refuse to believe it. Though the arguments in favor of such impos- 
sible statements may be swaying, we are not convinced. Why? Our 
experience of fife is the driving force of our belief systems. We become 



The Mind's Eye 1 



Joe Mazur 



so accustomed to what we believe that we cannot believe otherwise. 
This is truer in simple mathematics than it is in other areas of thought. 
Outside the world of mathematics, we often form beliefs and opinions 
that have little to do with factual trttth. Scientific truth involves ex- 
traordinarily complex procedures and evidence that often surprise even 
the most experienced investigators. 

Can We Believe What We See? 

Even truths that are seen through the eyes can be called into ques- 
tion. When Galileo discovered four new moons orbiting Jupiter, he 
was admonished because he had observed them with the help of a 
telescope and had not deduced them from logical arguments. Here is a 
case where someone is seeing the moons of Jupiter and is told that 
what he is seeing cannot be true, because logical argument is better 
than direct observation. Listen to how Galileo is mocked by the 
Florentine astronomer Francesco Sizzi: 

"The Jews and other ancient nations, as well as modern Eu- 
ropeans, have adopted the division of the week into seven 
days, and have named them from the seven planets: Now if 
we increase the number of planets, this whole system falls to 
the ground. . . . Moreover, the satellites are invisible to the 
naked eye and therefore can have no influence on the Earth 
and therefore would be useless and therefore do not exist." 
(Holton 691 

Galileo was actually seeing the moons of Jupiter with his own eyes, 
albeit through a telescope. Anyone could have seen the moons had he 
or she just looked! Extraordinary! Almost 400 years ago, a relatively 
short time ago, persuasion by logical argument or philosophical prin- 
ciples was considered stronger than persuasion by direct observation. 
Even seeing through the human lens and retina would have been 
considered indirect observation; so, surely, louking at the moons of 
Jupiter through a telescope was even more indirect. Yet, for us, we 
accept what we see as if it were truly direct observation. We even go so 
far as to trust radio waves to bring us pictures of the moon, of Mars 
and of the bottom of the Black Sea! Why aren't we more doubting? 

There are those who refuse to be persuaded, even in the face of 
enormous evidence. There are conspiracy theorists who believe the 

8 The Mind's Eye 



Joe Marur 



NASA moon landing was a hoax; they interpret evidence to support 
their own radically revisionist opinions. In fact, these conspiracy theo- 
rists were able to persuade the Fux Broadcasting Company to air a 
special broadcast on the subject. Although the broadcast disclaimed 
any bias, it withheld information that would have been useful to make 
reasonable judgments against the conspiracy theory. The program 
claimed that 20 percent of all Americans believe we never landed on 
the moon. Is that possible? Sure, Americans rely on printed and broad- 
cast media to shape their beliefs. When a highly advertised special on 
a major television network puts forward an allegedly convincing story 
in support of conspiracy, the opinions of its viewers tilt to support the 
possibility of conspiracy. Conspiracy theorists claim that the entire 
mission was Filmed in a studio, that Neil Armstrong never went to the 
moon and that thousands ot NASA scientists have been part of the 
conspiracy lor the past 32 years. And what is the evidence? Photo- 
graphs of Armstrong show two shadows, even though the sun should 
have been the only source of fight: so the other source must have 
been studio spotlights. The photographs show no stars, no blastoff cra- 
ter and a waving American flag. 

Surely, if the mission were a hoax, at least one of the thousands of 
NASA scientists would have thought of these faults, It turns out that 
every one of the objections has a scientific explanation that escaped 
the conspiracy theorists: There should have been more than one source 
of light (the reflective surfaces of the earth and moon), there should 
not have been stars visible in the photograph (stars need a lime expo- 
sure to appear in a photograph), the Lunar Landing Module should 
not have left a visible crater (moon dust is only a couple of inches 
thick) and flags wave when their poles are disturbed. In fact, a hoax 
would have been more likely had there been only one light source, 
stars in the photograph, a blastoff crater or a nonmoving flag. Perhaps 
it is easier to believe the mission to be a hoax than to comprehend 
how difficult it really was. How would Francesco Sizzi react to the 
NASA pictures? 

We tend to believe what we see with our own eyes, and we con- 
firm or deny facts according to what we sec, but we see ideas only 
through our minds' eyes. So David Hume divided all objects of hu- 
man reason and inquiry into only two categories, "relations of ideas" 
and "matters of fact" (Hume 40). Mathematics falls under the rela- 



The Mind's Eye 9 



Joe Mazur 



tions of ideas category and all other inquiry falls under matters of fact, 
which implies cause and effect. The Pythagorean theorem relates the 
sides of a triangle; arithmetic is about relations between numbers. Such 
mathematical inquiries, Hume claimed, involve thought that is inde- 
pendent, of the universe: 

Though there never were a circle or triangle in nature, the 
truths demonstrated by Euclid would forever retain their 
certainty and evidence. (40) 

In contrast, objects of matter of fact come from our experience with 
cause and effect. Hume suggested that we become accustomed to ac- 
cepting what we know as if that knowledge has come through reason, 
even though it really sneaks in through experience. We anticipate 
events such as the sun rising, fruit rotting and billiard balls colliding 
without concern about being wrong simply because we have seen the 
effects and not because we have reasoned from a priori assumptions. 
At times we form beliefs that are so self-convincing that we take stands 
based on what we expect from past observations: 

Such is the influence of custom that where it is strongest it 
not only covers our natural ignorance but even conceals it- 
self, and seems not to take place, merely because it is found 
in the highest degree. (41) ' 

Why do we believe that the earth is "round"? Couldn't it just as well 
be a drum? At one time, great thinkers saw the earth as a drum float- 
ing on water. Did you ever wonder and think about why you don't 
think so? At what point in your life did you come to believe that the 
earth was roughly a sphere revolving around the sun? If you were 
born after Apollo 7 sent back the first photographs of the earth rising 
over the moon, it's likely that you feel that the earth is not a drum 
floating on water. But what if you had never seen such photographs? 
At some point in your life, you came to accept, without question, that 
the earth is roughly spherical and to think that the drum image is 
primitive. How did you acquire the feeling that the earth is more spheri- 
cal than cylindrical? Why do you think that it does not float on water? 
What would your position be if for the past year you heard a barrage 
of media news telling you that scientists had discovered that the earth 
is really a drum floating on water? What if scientists at NASA agree 

10 The Mind's Eye 



Joe Mazur 



and there is no contest among all the most respected astrophysicists? 
What if you grew up hearing such impressions of the truth with asso- 
ciated images of the earth? Since our ancestors had notions that were 
different from ours, it must be that notions about the shape of the 
earth are taught. But can you think of a time when you didn't know 
that the earth was spherical? And can you think of a time when you 
didn't know that two points determine a straight line? 

. . . and here, as at the first of time, we lift our heads. 

Over us, more beautiful than the moon, a 

moon, a wonder to us, unattainable, 

a longing past the reach of longing, 

a light beyond our light, our lives — perhaps 

a meaning to us . . . 

O, a meaning! 
over us these silent beaches the bright 
earth, 

Presence among us (Macleish 1) 

Emmanuel Kant had something to say about this. The first line of 
his introduction to the Critique of Pure Season says that "there can be 
no doubt that all our knowledge begins with experience." fn the next 
paragraph, Kant says that "though all our knowledge begins with ex- 
perience, it does not follow that it all arises out of experience." He 
goes on to suggest that every human being possesses an a priori uni- 
versal knowledge that enables him or her to synthesize the impres- 
sions of the senses so that they transform into the things that we think 
we know. We don't notice the component parts of our reasoning be- 
cause we have become so accustomed to the way we think that we 
can no lunger distinguish the difference between what we perceive 
and what we infer. Or perhaps we are not aware of our reasoning 
process because it is so automatic. Kant borrows this example from 
geometry: The figure that is bounded by three straight lines is imme- 
diately known to have three angles; but the fact that the sum of those 
angles is two right angles is something that cannot be known without 
being inferred, f suppose that the immediacy of knowing that the three 

The Mind 's Eye 1 1 



Joe Mazur 



straight lines have three angles is a priori knowledge. But this knowl- 
edge is not limited to mathematics. 

Belief Can Alter Memory Just as Well as Memory Can Drive 
Belief 

Some time ago. while writing stories about my childhood, I re- 
called meeting an extraordinary man. 1 was eight or nine years old 
when 1 witnessed him performing an extraordinary stunt on a street 
corner near where 1 lived. He worked for the circus and had the as- 
tounding ability of being able to stand on one finger. But something 
even more extraordinary happened in recalling the event: t was not at 
all sure that 1 really had encountered the man! Could my memory 
have played a trick? Could anyone possibly stand on a single finger? 
Was it a dream? Could there have been a Mr. Unis? My memory seemed 
to have concocted a quasi-mythical figure. 

Several years after writing my stories, I attended a circus perfor- 
mance; It was a special performance on the 1 00th anniversary of the 
Ringling Brothers Circus. I was sealed high in the stands of the Boston 
Garden (now the Fleet Center), where, once again, I saw the very 
same Mr. Unis. He was not only standing on one finger but also bal- 
ancing himself on the end of a 30-foot pole! I was astonished! My 
quasi-mythical figure was not a fantasy! Allhough 1 still lound it diffi- 
cult to believe that my meeting with Mr. Unis was real, I became more 
convinced that it was, Still, there was a shadow of a doubt caused by 
the sheer physical impossibility of the stunt. When I was younger, I 
could have believed that a man could balance himself on one finger. 
Yet once a better knowledge of physics replaced my naive understand- 
ing, it became very difficult to believe in things like magic, spirits and 
humans standing on fingers. 

It might seem that we become convinced by repeated exposure to 
what we see and accept. But it's not that simple. I spent five years 
taking care of my wife after she had been in an automobile accident 
involving a truck that ran into her. I saw the accident happen and 
replayed it in my mind over and over again, thousands of times over a 
five-year period. What 1 saw in my mind was an enormous covered 
truck that was loaded with large boxes. The case went to trial. But in 
preparation for trial, I was given a picture of the truck, It was a shock 
to see that it was merely an unloaded three-quarter-ton pickup. The 

12 The Mind's Eye 



Jot Mazur 



iruck had such a devastating effect on my life that I had "monsterized" 
its image. It was a fiction of my imagination. 

"Look, memory can change the shape of a room. It can change 
the color of a car. And memories can be distorted. They are 
just an interpretation, not a record; and they are irrelevant, 
if you have the facts."' 

Hume put it succinctly this way: "Belief is something felt by the 
mind, which distinguishes the ideas of the judgment from the fictions 
of the imagination" (63). But this definition leaves much to be ex- 
plained. It is those "fictions of the imagination" that generally seem to 
have severely strong influences on "the ideas of our judgment." Each 
example above summons those fictions of our imagination to In- 
fluence the ideas of our judgments. The century we live in renders 
support to Galileo's observations. And what are we to make of the 
conspiracy theory example? 

Images of a collapsing World Trade Center are burned into our 
brains. Passing associations trigger the implausible pictures, while we 
say, "No, that didn't happen!" Our minds refuse not only to believe 
that humans arc capable of such heinous acts but also to believe that a 
building so tall and wide can collapse. After all, didn't the 1993 bomb- 
ing prove that the World Trade Center was indestructible? The World 
Trade Center collapsing? Isn't that impossible? My brain still has a 
hard time believing it. My beliefs are still in conflict with what I saw 
on television. After all, isn't television just an advanced extension of 
Galileo's telescope? 

If there is a distinction between the ideas of the pure judgment 
and the fictions of the imagination, how fine or strong is that distinc- 
tion? Mathematics has a reputation for being a pure judgment totally 
distinct from fictions of the imagination, but is it really? For the mo- 
ment, let us explore how experience ignites the process that drives 
opinion to persuasion. 

We communicate using statements of some doubt, statements we 
unquestionably believe and statements that we accept on authority. 
Of course, there are statements that we cannot judge — we don't doubt 
them and we don't support them. There are also statements that may 
be true to one observer and false to another. For example, take the 
statement "Tears are mixtures of water and sodium chloride." If you 



The Mind's Eye 13 



Joe Mazur 



are a poet, painter, fiction writer or psychologist, you may not agree. 
So is it true that tears are mixtures of water and sodium chloride? 

We generally communicate through statements that include words. 
"Blue is a color" is a proposition that may be true or false. But "x is a 
y" is a proposition in form only; it has no sense of truth or falsity until 
both x and y are replaced by words that have meaning. Logicians call 
the statement "x is a y" a prepositional function. Its truth or falsity en- 
tirely depends on the words substituted for the variables x and y. The 
trouble is that discourses often contain undefined or ambiguous terms 
that make propositional functions meaningless, though the speakers 
most likely intend them to be real propositions. For example, the state- 
ment "Tears are mixtures of water and sodium chloride" is not a propo- 
sition, because it contains a word that has several meanings. We can 
even say different things using the same words. An advertisement of 
Travetocity.com reads "Go virtually anywhere." Permute the words to 
say "Virtually go anywhere" or "Go anywhere virtually" and you have 
different meanings. 

Ideas are the profits of ambiguities. Words of informal languages 
such as English are blessed with ambiguities of meaning, leading to 
misinterpretations of truth on the one hand and the creation of new 
thoughts on the other. These misinterpretations account for at least 
part of the reason there are so many arguments and disagreements 
among people of the same culture. Formal languages, on the other 
hand, such as computer programming languages and symbolic logic, 
talk about x being y, and therefore can express definitive conclusions 
based solely on Formal relations among the variables, even though 
those variables have no meaning at all. 

To make things more complicated, our beliefs may simply be 
influenced by our culture or our ignorance. Take, for example, "A 
four-leaf ctover is very hard to find in a field of clover." You may be 
convinced that it is true because you have heard that a four-leaf clo- 
ver is a lucky find. But have you ever tried to find a four-leaf clover in 
a field of clover? If you haven't, how do you know that it is hard to 
find? Andrew Weil relates a wonderfuf story to suggest that belief is a 
strong influence on what we see. He writes: 

Years ago I met a woman who was able to find four-leaf clo- 
vers in any clover patch. . . . When I would look through 

14 The Mind's Eye 



Joe Mazur 



patches of clover, I could search without success until my 
vision blurred, and whenever I thought I saw four leaves on 
one stem. They always turned out to belong to two different 
clovers. But after meeting this woman and watching her do 
it, something changed for me. 1 realized that the key to her 
success was her belief that in any clover patch there was a 
four-leaf clover waiting to be found. With that belief, there 
is a chance of finding it; without it there is none. After meet- 
ing her, I began to look again, and soon I started to find four- 
leaf clovers. (195) 

When I was a graduate student, an apocryphal story about the 
mathematician John Milnor circulated around the mathematics com- 
munity. One day, when Milnor was an undergraduate at Princeton in 
the early fifties, the story went, he came late to Ralph Fox's Differen- 
tiate Topology class. Fox had written on the blackboard a list of ten of 
the most outstanding unsolved problems of mathematics. Milnor 
copied the problems, thinking that they were part of the next 
homework assignment. At the next class session, Milnor, bash- 
fully embarrassed, told Fox that he had solved nine of the ten home- 
work problems but could not get the tenth. Nobody really believes the 
full truth of this story, though it is more than likely that some limited 
version did happen. The point is that Milnor had two significan t advan- 
tages: One was his extraordinary mathematical talent; the other was 
that he was not handicapped by any severe sense of difficulty. 

Belief is so empowering that it can not only control success but 
also alter one's future. There are two components to the art of for- 
tune-telling: a vagueness that is open to interpretation and the client's 
willingness to believe. It is this willingness to believe that, through the 
power of the mind, can override any vagueness and twist the inter- 
pretation to fit whatever happens in the future. The Bellman in the 
Lewis Carroll nonsense poem "The Hunting of the Snark" believes 
that what he tells his crew three times is true, fndeed. for many of us, 
it may be true that we believe what we hear often enough. 

"Just the place for a Snark!" the Bellman cried, 
As he landed his crew with care; 
Supporting each man on the top of the tide 
By a finger entwined in his hair. 



The Mind's Eye 15 



Joe Mazur 



"Just the place for a Snark! I have said it twice: 
That alone should encourage the crew. 
Just the place for a Snark! I have said it thrice: 
What I tell you three times is true." ( 1 82) 

It's not just what is told three times but also what one wants to be- 
lieve. So the fortune-teller concocts a future that includes not only 
possible experiences but also probable ones. Successful predictions 
simply depend on willful interpretations, wishful thinking and the 
passage of lots of time. Include lots of time and you have a high prob- 
ability that the future will be coincident with the fortune. There is not 
only a mind-body connection but a mind-future one as well. 

Feeling Belief 

To say of what is that it is not, or of what is not that it is, is 
false, while to say of what is that it is, or of what is not that 
it is not, is true. — Aristotle, Metaphysics 

Seventy-five years after Camille Jordan finished a proof of his theo- 
rem on curves in the Cafe Luxembourg, I found myself in the same 
cafe with another great prolessor. As an American studying in Paris, I 
had not been informed of the great reverence that the French had for 
professors and was dumb enough to simpiy confront mine with ques- 
tions. Normally, a professor would lecture to a very large audience 
after entering the lecture hall from an anteroom at the back of a stage 
filled with microphones. At the end of the lecture, he would leave 
through the same anteroom, not questioned and not seen again by 
the students until the next lecture. 

One afternoon, in October of 1961, 1 was walking along the Bou- 
levard St. Michel with several French friends when I spotted Professor 
Roger Godement walking toward us. My friends were so nervous about 
the proximity of God himself that they immediately crossed the street 
to give him more space. On seeing this strange foreign behavior, I 
decided to play it for what it was worth and stopped Professor 
Godement in his tracks. Of course, he didn't know me. I simply said 
what any courageous American student would say upon meeting his 
or her professor: "Hello, Professor Godement. I am a student in your 
algebra class and wonder if f could meet with you sometime to clarify 
the proof that you talked about in today's class." 

16 The Mind's Eye 



Joe Mazur 



To my great surprise, his answer was what any reasonable Ameri- 
can professor would have given under the circumstances: "Sure, why 
don't we have a coffee in that cafe across the street and I will tell you 
all about it?" Well, perhaps reasonable American professors wouldn't 
say this, but at least in America it would not be a surprise if one did. I 
was not prepared for such a generous offer, but immensely enjoyed 
witnessing the shock and surprise portrayed on my friends' faces as 
the Great Professor and I crossed the street and entered the Cafe Lux- 
embourg. 

We sat in the cafe for more than an hour while Professor Godement 
explained the proof in detail. At that first meeting, he was as nervous 
as I was, but we met at that same cafe several times during the year. I 
believe we mutually enjoyed our meetings, because he had a rare 
chance to talk with an undergraduate and I had the chance to show 
off to my friends. One day Professor Godement turned to me and calmly 
said, "You know, about seventy-five years ago, Camille Jordan proved 
this very same theorem in this very same cafe." 

"'Tis the note of the Jubjub! Keep count, I entreat; 
You will find I have told it you twice. 
'Tis the song of the Jubjub! The proof is complete, 
II only I've stated it thrice." (Carroll 197) 

I first heard the story of Professor Jordan's curve from James 
Charmer, my high school geometry teacher. It would have been to- 
tally forgotten had Roger Godement not revived it on that afternoon 
in October 1961. 1 hadn't believed Charmer's story before the first 
time I ordered a croissant at the Luxembourg; Without my asking for 
it, the waiter brought me peach jam. 

My first serious introduction to modern mathematics was through 
Professor Godement's course in modern algebra at the University of 
Paris, He stated theorems and proved them, one after another. For 
the first six months of attending his classes, I felt a strange sensation of 
both understanding the proofs and not knowing why. Some proofs 
were long, others short, but they were almost all informally worded. 
Occasionally, the words would form neat sequences of statements that 
would make the proof easier to follow, but mostly they were rough 
and unpolished. Yet I understood the overall effect of the argument or 
proof. For years after, I puzzled over the question of why I could un- 



The Mind's Eye n 



Joe Mazur 



demand and believe that one statement follows another without be- 
ing told any of the rules. It seemed as if my brain were wired to accept 
the rules and that learning them was never necessary. It became clear 
to me then that there were no fixed rules. 

What makes an argument believable? How do we become con- 
vinced? In high school, I was taught to mimic proofs that were spelled 
out in geometry texts. You know the kind: "Prove that two triangles 
that have their corresponding sides, angles and sides equal are con- 
gruent," I was taught to believe that there is some absolute, structural, 
logical inference that was necessary in order to accept an argument as 
valid. But real mathematicians don't talk in absolute logical structures. 
Texts in my high school days misled students to believe that math- 
ematical, proofs come from a well-defined process, as opposed to an 
artful means of communication. Mathematicians communicate with 
one another by vague symbolic gestures that indicate what should 
lollow from what was just said. A squiggly mark may represent an 
"Abelian variety," which is an object that has a complex definition. 
Somehow, it immediately makes perfect sense in conversation between 
two mathematicians who have experience with Abelian varieties, just 
as a roughly drawn picture of a triangle might represent a triangle. 

Pictures of Truth 

Anticipations are a ground sufficiently firm for consent, for 
even if men went mad all after the same fashion, they might 
agree one with another well enough. — Francis Bacon 

I recently heard a philosopher lecture on visual reasoning in math- 
ematics. Pew in the audience had any experience with mathematical 
proofs, beyond those that they had seen in their high school geometry 
classes. The audience included anthropologists, philosophers, poets, 
psychologists, historians and professors ol literature, among others. 
"We may use pictures to convince us of the truth of many kinds of 
claims," the speaker began. "They are used in geometry classes to show 
us how to prove mathematical claims," she continued. "Can pictures 
be considered actual proofs, or are they merely used as symbobc icons?" 



18 The Mind's Bye 



Joe Mazur 



A statement was displayed together with a picture: 

Statement 1 : The sum of the first n odd integers is equal to the square of 
n; i.e., 1 + 3 + 5 + "' + (2n - 1) = n 2 . 



Figure 1 

The speaker suggested that the picture (figure 1) is more convincing 
than the statement, not only because it is convincing but also because 
it naturally leads to the more formal proof. 

She then displayed another statement and a picture of a line of 
length 1 (figure 2) with divisions in increments of 1/2" and asked if it 
proved the statement 

111 1 

Statement 2: — + -j + -g + - + y n + - ; 

1 1 1 J. 

T 4 8 16 

t "~ r " r^r* 

Figure 2 

Almost everyone in the group felt that figure 2 proved statement 2 
because, as someone said, "the space left between the end of the line 
and the nth marker was getting smaller and smaller as n increased." 

But when the following picture was displayed, everyone rejected 
it as a proof that "1 equals 2," (The picture is supposed to depict an 
infinite sequence of "sawtoothlike" figures that converge to a line; 
that is, the sawtooth edge smoothens out to become the line.) 




The Mind's Eye 19 



Joe Mazur 



Total length ttf 




always equals 2 

Total length of 
vertical lines 
■i- always equals 1 



Continue the process 
indefinitely. You see 
that the jagged edge 
approaches the vertical 
line 



J 



Figure 3 



The general consensus was that one could not assume that the 
slanted lines would actually approach the straight base line even after 
an infinite numher of iterations of the construction. The interesting 
thing here is that, although the majority of the audience was perfectly 
willing to accept the picture in figure 2 as proof of statement 2 (rea- 
soning that the remaining space shrinks to zero as n grows large), it 
refused to accept the picture in figure 3 as proof that 2 = I. Of course, 
one reason for the heightened suspicion is that we know that 2 is not 
equal to 1, and that knowledge psychologically conditions us to sus- 
pect that the picture is misleading. However, if figure 2 implies state- 
ment 2 for the reasons given, then we must also accept that figure 3 
implies that 2 = 1. 

Figure 2 is persuasive but not convincing; we cannot tell if the 
infinitely many small segments will fill the space or overshoot it. un- 
less we examine the sum of fractions itself. Perhaps it is not fair to 
present pictures of infinite processes to a general audience, because 
one inevitably will fantasize, rather than see, what happens in the 
infinite tail of the picture. 

This leads to the question of how to define "picture." What do we 
mean by "picture"? What is the difference between the pictures on 
the left and the corresponding pictures on the right (below)? We have 
an intuitive understanding of what it means to add two numbers. 
Therefore, I think you will agree that the pictures on the left give the 

20 The Mind's Eye 



Jce Mazur 



same mental impressions as those on the right. But the picture on the 
right seems to tell us something: It gives us an impression that the 
sum of 1, 3 and 5 is a perfect square. 



1 



3 



5 



1+3 + 5 



Interpretation of a painting will bank on flexible meaning, inter- 
action, history and culture. What you see is what you interpret. But 
if this picture were a mathematical object, there would be no flexibil- 
ity in interpretation — what you see must lock into a fixed universal 
definition. A good poem may also provide flexible interpretation, but 
since it is composed of words that have meaning, it provides a tighter 
feeling of interpretation. 

A little, pretty bird 
Took his flight. 
Toward the garden 
Where was fruit a-plenty. 

If I a pretty 
Little bird could be, 
I would not hesitate; 
I'd do the same as he, 

Limetwigs' cunning 
Lurks in such a place. 
The poor bird 
Could no more escape. 




The Mind's Eye 21 



Joe Mazur 



If I a pretty 
LitlJe bird could be, 
I would hesitate indeed, 
I'd not do as he. 

The bird came 

Into a lovely hand, 

There he fared. 

The happy one, the same. 

If I a pretty 
Little bird could be. 
I would not hesitate; 
I'd do indeed as he. 

—Johannes Brahms, "A Pretty Little Bird" 

What could be fell in reading this poem? Surely, there is a feeling, 
a feeling for the bird, and a feeling in you the reader, who has identi- 
fied with the bird. And whose "lovely hand" do you imagine it to be? 
As you read this poem, images are conjured up in your mind. But 
there is more! There are feelings both for the bird and for the person 
with the lovely hand — you, perhaps. Did I call it a poem? Actually, it 
is a song written by Brahms. If you could hear it sung, it would add 
another dimension to your feelings. Reading and hearing the song 
invokes complex sensations that trigger pictures to imagine, which in 
turn, stimulate feelings of thought. 

Good pictures can invoke plenty of useful imagination, insight 
and even understanding, but more often than not, can lead nowhere 
or even mislead. Lewis Carroll plays with this thought in "The Hunt- 
ing of the Snark" where the Bellman presents a map of the sea: 

He had bought a large map representing the sea. 

Without the least vestige of land: 
And the crew were much pleased when they found it to be 

A map they could all understand. 



22 Tke Mind's Eye 



Joe Mazur 



"What's the good of Mercator's North Poles and Equators, 

Tropics, Zones, and Meridian Lines?" 
So the Bellman would cry: and the crew would reply 

"They are merely conventional signs!" 

"Other maps are such shapes, with their islands and capes! 

But we've got our brave Captain to thank" 
(So the crew would protest) "that he's bought us the best — 
A perfect and absolute blank!" (185) 

See picture of the Bellman's map below. 

NORTH 



m 
I 



SOUTH Scale of miles 

I 1 

100 Mi 

Ocean Chart 



One Can't Believe in Impossible Things, Can One? 

Alice laughed: "There's no use trying," she said; "one 
can't believe impossible things." 

"1 daresay you haven't had much practice," said the 
Queen. "When 1 was younger, I always did it for half an hour 
a day. Why, sometimes I've believed as many as six impos- 
sible things before breakfast." 

— Lewis Carroll, Alice's Adventures in Wonderland 



The Mind's Eye 23 



Joe Mazur 



Is there a feeling to being convinced of an argument? We nor- 
mally associate feelings with pleasure or pain, or any of the other senses 
of the skin triggered by touch, but a more general meaning includes 
mood and emotion. What did Hume mean when he said, "Belief is 
something felt by the mind"? To push it further, it can also be con- 
nected to thinking and belief, or doubt. One may say, T'feef that I am 
right," when faced with a belief. What do we "feel"? Surely, we don't 
"feel" belief or doubt through physical sensation. The feeling of pain is 
physical and can be measured by degree. We can describe and distin- 
guish mild pain from torture. To a lesser degree, we can even describe 
and distinguish pleasure from ecstasy, So is there a "feeling" of being 
right or wrong? Can I "feel" that 1 am right? And can we attach 
weights to the -feeling" of being right? Can I "feel" that I am right 
but still "feel" a bit uncertain? What do I "feel" when I encounter the 
impossible? 

It's not often that one encounters the impossible. So what would 
your mind "feel" if one day you were having a picnic in the forest and 
saw a woman riding a horse? Nothing unusual. But what if this horse 
and rider could be seen only when they were behind a tree and could 
not be seen when there was nothing to obstruct the view? Such a 
scene is depicted in the Rene Magritte painting Carte Blanche. Besides 
being startled, you would respond by denying what you were seeing 
with your own eyes, fn a sense, you would be feeling just what 
Francesco Sizzi felt when he mocked Galileo's observation of an eighth 
planet. From his experience, seeing the eighth planet was like seeing a 
woman riding a horse with the background swapped with the fore- 
ground. Even newborn infants stare in surprise when an object disap- 
pears or appears to pass through another. You cannot believe in im- 
possible things! 

"Who'a ya gonna believe, me or your own eyes?" 

— Chico Marx 



24 The Mind's Eye 



Joe Mazur 




The Ames Room 



Although I learned the rules of perspective drawing from a pro- 
fessional illustrator, and even taught perspective drawing as part of a 
projective geometry course, I could never find a truly mathematical 
way to fix the correct impression of depth along vanishing lines, ft 
turns out that there really is no way, because perspective relies on the 
projection of points that come from rays emanating from a single van- 
ishing point, and a projected point on a ray could have come from any 
point along that ray. Parallax is not the correct answer to how we are 
aware of depth, for it does not explain how we falsely perceive the so- 
called Ames Room," a room constructed in such a way that a short 
person appears taller than a tall person does. But how does the mind 
perceive such false readings? Surely, when we walk into a familiar 
room, we have a preconceived sense of its space and that sense gets 
registered somewhere in the brain as an expected space, a room where 
floors, walls and ceilings make right angles with each other. We very 
rarely see rooms that are built to deceive us. So the mind records "room" 



The Mind's Eye 2 5 



Joe Mazur 



and interprets the vision to follow what it expects a room to look like. 
Should you encounter a room like the Ames Room, your conscious 
thinking machinery will suggest that something is impossible while 
your brain continues to interpret the scene exactly as your eyes see it. 
Yon think that what you see is impossible, yet your brain Insists that 
that is what your eyes are truly seeing. Ames constructed such per- 
ceptual tricks to demonstrate that our perception of the world is largely 
shaped by experience with our environment. If you stand at the edge 
of an ocean and look out at a rock jutting out from the sea, you will 
find it difficult to say how far away the rock is, unless there is a boat or 
a person near the rock. Your measure of the distance will be what 
your mind expects it to be, based on the size of the image of the boat 
or person. The brain has seen rocks of all sizes, so it has no fixed idea 
of its measurement. But your experience of the range of sizes for man 
or boat is reiatively limited, so the brain can use those ranges to com- 
pute what the distance from you to the rock should he. 

It may be true that parallax, the geometric computation of depth 
using a pair of eyes focusing on objects in the distance, is one of the 
brain's tools for perceiving depth, but the brain also has a backup plan. 
In fact, the brain continuously computes depth from probabilities based 
on information supplied by experience with the visual field. What this 
means is that the brain does not necessarily rely on one method of 
information processing but can resort to a variety of alternatives should 
it need to do so. It also means that our physical experience plays an 
enormous role in how we intuit new things. It could also mean that 
our logic depends on the continual bombardment of cause-and-effect 
experiences of the past. But coincidences often confuse those experi- 
ences. Toistoy suggested that some people are quick to link effect to 
cause when the real connection is simply coincidence: 

The peasants say that in the late spring a cold wind blows 
because the oak-buds are opening, and, as a fact, a cold wind 
does blow every spring when the oak is coming out. But 
though the cause of the cold wind's blowing just when the 
oaks are coming out is unknown to me, I cannot agree with 
the peasants the cause of the cold wind is the opening of the 
oak-buds, because the force of the wind is altogether outside 
the influence of the buds. (768) 

26 The Mind's Eye 



Joe Mazur 



We are bombarded with such compelling connections daily and our 
vulnerable impressions arc constantly competing with the forceful 
powers of coincidence and the convenience of its inert preference for 
acceptance. Again, the mind has amazing capabilities for changing its 
own mechanisms. [ can think about thinking and think that I should 
think differently, though it is not always an easy thing to do. 

When we view an Ames Room, we see exactly what we are sup- 
posed to see. We see the true visual field that is in front of our eyes. 
But we lose a sense of measure: We can no longer see two equal things 
as equal. So what is true? Yes, the two figures in the Ames Room may 
be the same height, even though we do not see them as being the 
same height. And yet we see exactly what is really there I 

So the mind has a big task: to interpret perceptions of the world so 
that the body can live without contradictions. What we see with our 
eyes does not necessarily have to be truly what exists; it has only to be 
consistent with how the world moves. There are solid objects out there. 
We can perceive them in any old way, as long as we don't crash into 
them and create havoc. If I drive through an intersection and don't 
see a truck crossing in front of me, I am in trouble. Do I not see it 
because it is not there, or do I not see it because it is there and I per- 
ceive it to be a hundred feet away from where it really is? If I walk 
through the woods and see someone riding a horse in a background 
confused with foreground, does my brain reinterpret what I am see- 
ing so that the world makes sense, or are the horse and rider really 
woven between the trees in the background and the trees in the fore- 
ground like the horse and rider in a Magritte painting? 

When I look into the Ames Room, I instantly know that what 1 
am seeing is an illusion, that m y eyes a re deceiving me and that I must 
think of some reason why I am seeing something false. In other words, 
the brain knows something that the eyes don't. 

So why shouldn't we expect our mathematical intuition to work 
the same way? It's reasonable to suppose that it comes in cycles built 
from syntheses of compelling logic schemes, experiences with the 
environment and more primitive mathematical intuitions. We can 
imagine things that do not really exist in the physical world, such as 
Platonic triangles. How? Typically, we do it by picturing any old tri- 
angle and ascribing the mathematical properties of a triangle to it. I 



The Mind's Eye 27 



JoeMazur 

may have learned in grade school that a triangle is a figure with three 
sides and three angles. After learning thai, I probably found out that 
the sum of the angles of any triangle is 180 degrees. Much later [ learned 
about the properties of right triangles, the Pythagorean theorem, the 
law of cosines, etc. Every thought of a triangle changes my intuitive 
concept of triangleness. The triangle that 1 see in my mind's eye must 
be interpreted to make mathematical sense. It may be a figure that has 
no straight lines! Or it may be a figure that looks like a lady riding a 
horse through a Magritte woods! What I imagine doesn't matter, if my 
brain interprets the image in a way that makes mathematical sense. 

When I hear some false argument about a triangle, I may not be 
able to immediately pinpoint what part of the argument is fake, but I 
know that some part is false. My brain will not accept the argument. 
To refute Lewis Carroll's demonstration that all triangles are isosceles, 
we need only exhibit one triangle that is not isosceles; but few persons 
can pinpoint the place where his argument breaks down. Carroll's ar- 
gument uses a little trick, well known to magicians. It gets us to look 
away for a moment. His argument deals with two cases; and it is true 
that there are only two cases: Either a certain two lines meet or they 
don't. Hey, what could be more representative of the faw of the ex- 
cluded middle? 5 So we walk away thinking that we have fully investi- 
gated the only two possible cases. And we have! But where do those 
two lines meet? We are fooled into following the picture that he pre- 
sents, with an intersection point inside the triangle, while all the while 
the intersection point may have faflen outside the triangle. 

Could Professor Jordan Have Been Wrong? 

Search in and out and round about. 

And you'll discover never 

A tale so free from every doubt — 

All probable, possible shadow of doubt — 

All possible doubt whatever! 

— Gilbert and Sullivan, The Gondoliers 



28 The Mind's Eye 



Joe Mazur 



Just when Camille Jordan thought he had completed his lengthy 
proof, Giuseppi Peano, teaching at the University of Turin, invented a 
peculiar curve. Professor Peano's strange object satisfied all the tradi- 
tional requirements of the definition of a curve but was so peculiar 
that even Camille Jordan had not accounted for it in the proof of his 
theorem, Peano's invention put a hole in Jordan's proof. So Jordan 
went back to his favorite cafe and scribbled out another hundred pages 
of proof to accommodate Peano's invention. Again, what Jordan 
thought was true in October of 1S86 was true, at least for the time 
being. And once again, the story does not end here. 

On first glance, you might say, just as Jordan did, that "of course 
this theorem is true!" Trouble comes only when you try to use your 
intuitive experience of space to prove something that depends on pre- 
cise definitions. We tend to confuse the spatial model of a curve with 
the abstract definition of a curve. We haven't seen all the possible 
contortions that Jordan's curves could go through. But more impor- 
tant, we don't even know what a curve is! 

Twenty-three-hundred years ago, mathematicians and philoso- 
phers struggled with the idea of defining terms such as point, line and 
circle, mathematical objects that come from experiencing our spatial 
world. Euclid decided to define a point as "that which has no part." 
Not a very satisfactory definition from a modern point of view, but 
surely one that is better than Plato's; "A point is that of which the 
middle covers the ends," whatever that means. (His definitions for 
straight line and circle are not much better.) 

Euclid's First Proposition 

Proposition One: An equilateral triangle may be constructed on a finite 
straight line AB. 

A ^^^^^™~ ~ J3 

To prove it, Euclid had to use five postulates to construct two circles of 
radius AB, one centered at A and the other at B, He then marked one 
of the points of intersection as P and constructed two lines, one from 
A to P and the other from B to P. 



The Mind's Eye 29 



Joe Mazur 




But what right did he have to assume that the intersection point P 
exists? How do we know that the two circles actually intersect each 
other? You would say, "How could the two circles not intersect?" If 
mathematics is axiomatic and a system of arguments that follow from 
each other, then we should not accept Proposition One as valid, for 
there is no argument that tells us that the intersection of the two circles 
used in the proof exists. The probfem is that we find it hard to believe 
thai the intersection does not exist. How could it not exist? Is there 
something to worry about? For more than 2000 years, we felt confident 
that the proof of Proposition One was valid. But it "feels" obvious that the 
two circles intersect, hi this sense, we "feel" truth. We "know" that the 
proposition is true, because we are so convinced; and the' small detail 
of conceiving a possible way for the two circles to not intersect should 
not really get in the way of our believing the proposition. 

And yet. . , ! 

Those circles arc imagined as part of the real world of circles. In 
the 1 9th century, mathematicians realized that the real world does 
not matter. Mathematical systems were invented without regard to 
the real world. We now know that the fifth postulate of Euclid could 
be replaced by a postulate that states that "there are no straight lines 
parallel to a given straight line." This may sound false; but if you 
replace Euclid's fifth postulate with this new one, you have a new 
system that is logically consistent and one that gives a whole new 
geometry. The geometry may not be that of the world we are used to. 
And so our intuition can play tricks on us. We have a much harder time 
accepting statements in this new geometry and must resort to checking 
things not by "feelings" of truth but by dear, logical inferences. 



30 The Mind's Bye 



Joe Mazur 



Jordan's Theorem Once Again 

Professor Jordan thought that his proof was correct. He accom- 
modated Peano's curve in the latest version of his proof and felt con- 
vinced that all was well. A year had passed while his proof circulated 
through the mathematical community. Alas, just when Jordan was 
feeling quite good about his theorem, David Hilbert, chairman of the 
Mathematics Department at the University of Gottingen, invented 
another anomalous curve that Jordan had not considered. Again, the 
proof was destroyed. 

The chronicle of Jordan's proof continues with several distinguished 
mathematicians of the time giving proofs that were eventually found 
to be incorrect. Oswald Veblen was 25 years old when he went to 
Princeton from Chicago. In 1905, f9 years after that one student in 
Professor Jordan's class hesitated to accept the statement as obvious, 
Veblen gave the first correct proof. It was only 1 5 pages lung (Veblen 
83-98). Once again, the theorem was shown to be true. But hadn't it 
been true all along? And if it had always been true, how could Jordan 
have known it to be true without having a solid proof? 

Jordan's story seemed to have no end. My belief in it came through 
totally coincidental events. Jacques Azerad, a man in his early 50s at 
the time of this story, was a professor of medicine at the University of 
Paris Medical School. Like his father, he was a distinguished cardiolo- 
gist. One day, while I was hitchhiking to class, a handsome man with 
a thick black mustache stopped his tiny three-wheeled vehicle to give 
me a lift. We arrived close to the university with time to spare for a 
beer at — of all places — the Gate Luxembourg, fn my awkward uneasi- 
ness and broken French, f told the story of Jordan's endless work at the 
cafe. Dr. Azerad politely listened with a gaze of excited interest, and 
when he learned that 1 was looking for an affordable apartment in Paris — 
to my great surprise — quickly offered a room in his apartment. 

In exchange for living with the doctor and his beautiful wife, I 
would be obliged to have Sunday suppers with them, and twice dur- 
ing the year — once at Christmas and again at Easter — to take a tour of 
Prance en route to the Azerad villa in St.-Tropez. We would take our 
Sunday meals at different auberges, generally outside Paris. My room 
on the third floor was small but bright, opening onto a courtyard with 
large trees and a view of the concierge's office below. A barber's chair 



The Mind's Eye 31 



Joe Mazur 



sat in one corner near the French doors, so I could spend long Sunday 
afternoons reading while listening to music and feeling the breeze 
through the lace curtains in front of the opened doors. 

As if fine dining every Sunday were not enough for my benefac- 
tors, I also had to accompany Jacques and his entourage to concerts 
and operas. For our out-of-town trips, we would stay in five-star ho- 
tels and gracefully drink fine wines at the level ot a 1945 Chateau 
Gruard-Laiose or a 1955 Chateau Montrose, f was not the only one 
living with the Azerads. Jacques had a habit of inviting fascinating 
people to live in his sprawling residence. A studio was specially built 
for Pierre Languet, a postexpressionist painter who had been carrying 
on a visibly open affair with Mme. Azerad, a brilliant professor of 
medicine who wore tight-fitting clothes to reveal her Junoesque body. 
Pierre was arrogant. He once rejected a bottle of Francis Darroze Bas 
Armagnac Aux Dues, just to see the reaction of a wine steward, who 
confidently waited for an opinion of the sample. There was Francois 
Merlot, a young dancer who debuted in West Side Story and spent part 
of the year in New York working for Alvin Ailey. Jean Paul Druhopf, 
first violinist with the Paris Orchestra, was in charge of our dining 
itinerary. Every Sunday at six p.m., we would meet in the foyer of the 
apartment for an aperitif before the evening out. 

To this day, f wonder why the good doctor was so kind to me, a 
total stranger. Months went by while f suspiciously pondered sinister 
motives. But he never asked for a favor in return. He simply took an 
interest in my studies and me. He regarded himself as being a patron 
of resident artists and scholars. I was his resident mathematician. 

"Meet my father," Jacques said to me when we arrived at his villa 
in St.-Tropez one day. 

A very thin, tall and distinguished old gentleman, with a slightly 
bent frame, extended a hand with a broad smile that suggested that he 
already had heard much about me, I greeted him while Jacques ex- 
plained that, though his father was a physician, he had studied math- 
ematics when he was younger. 

"Oh, yes," exclaimed the gentleman, "1 studied at 1'Ecole Polytech- 
nique, but that was long ago," 

At dinner that evening, I could think of nothing to say, and so 
chanced to tell the story of Camille Jordan, just as 1 had heard it twice 
before. He listened with great interest, expressing himself by tilts of 

32 The Mind's Bye 



Joe Mazur 



his head, strokes of his forked beard, brief smiles. When I had fin- 
ished, he glanced at Jacques and rhetorically asked, "That student who 
interrupted Professor Jordan to ask for more evidence?" 
"Yes?" I asked, expecting an answer. 

But an answer never came. If there were to be an answer, it would 
have to come from his continued broad smUe of delight that indicated 
it had been a long time since he had heard that story. 

The Beaver had counted with scrupulous care, 
Attending to every word: 
But it fairly lost heart, and outgrahe in despair, 
When the third repetition occurred. (Carroll 197) 



Notes 

1 The renowned Cours d'analyse de 1'Ecole Polytechnique. 

2 An isosceles triangle is a triangle with two sides of equal length. 

5 From the part of Leonard Shelby, the protagonist in Memento, a film 
by Christopher Nolan based on a short story by Jonathan Nolan. 

4 After the painter-psychologist Adelbert Ames, Jr. 

! A fundamental proposition of logic that says that something is or 
isn't, and that there is nothing in between. 



Works Cited 

Brahms, Johannes. LiebesliederWalzer, Opus 52. Trans. Philipp Naegele. 
Marlboro, VT: Marlboro Music Festival, 2001. 

Carroll, Lewis. The Complete Illustrated Works of Lewis Carroll. Ed. Ed- 
ward Guiliano. New York: Avenel, 1982. 

Holton, Gerald. Introduction to Concepts and Theories in Physical Science. 
Reading, MA: Addison-Wesley, 1952. 

Hume, David. An Inquiry Concerning Human Understanding. Ed. Charles 
W. Hendel. New York: Macmillan, 195 5. 

Maclcish, Archibald. Poem. New York Times 29 July 1969. 

Tolstoy. Leo. War and Peace. Trans, Constance Garnett. New York: 
Modern Library, 1950. 

Veblen, Oswald, American Mathematical Society Transactions 6. 1905. 

Weil, Andrew. Spontaneous Healing. New York: Knopf, 1995. 



The Mind's Eye 33 



Four Poems 

BY SARA LITTLECROW-RUSSELL 



Indian Territory 

Part I — Smells 

Horse shit drying on work boots, 

Sweetgrass and dollar cigarettes 

curling into aromatic spirals. 

Old star blankets releasing 

their stale mustiness into body beat, 

Slow-cooked commodity beans 

bubbling on a cast-iron stove, 

A warm road-kill deer being butchered 

on the kitchen floor. 

Part II — Tastes 

Old pots and pans brewing coffee 
tasting faintly of tinfoil, 
Raw beef kidneys 
dissolving slowly 
like gamy Jell-o, 
Melted, stolen candy bars 
sweeter than the tiny wild berries 
thai grow between the rusty cars. 

Part III— Sounds 

A truck engine 
grinds over and over. 
Fry bread sizzles in hot lard, 
An owl shrieks across the valley. 
High-voltage wires hum a lullaby. 
Bottles clink in the living room. 
Soon there are thuds against the wall 
as the fighting begins. 

34 The Mind's Eye 



Sara Littlecrow-Russel! 



Love Song from a Silent Flute 

You are the old beadwork 

That I mend with cautious, 

Needle -pricked fingers. 

You are burning chaga. 

Raw sweetness scraping my lungs 

And startling tears from my eyes. 

You are the bear-claw necklace 

No longer caressing 

The space between my breasts. 

You are the cigarettes 

That I quit years ago, 

But sometimes smoke anyways. 

You are the cedar branch 

That sweeps away my footprints 

And hides me from danger. 

You are maple syrup on snow 

Melting on my tongue 

Until I ache with cold. 

You are the eagle wing 

Sheltering me Irom 

An urban thunderstorm. 

You are the star blanket 

Sliding off the bed at night 

And leaving me shivering in the morning. 

You are the stubborn braid ol wiingashk 
That must be relit with a dozen matches 
Before it releases its thin streamers of sweetness. 
You are the love song that I play on a silent flute. 



The Mind's Eye 35 



Sara Liukcrow-Russell 



I Will Take Anyone to Bed 
(Poetically Speaking, of Course) 

I have made love with Pablo Neruda 
On the heights of Machu Picchu 
I flashed the tattoo on my thigh 
And hitched a iowride with Luiz Rodriguez 
I have held Adrian Louis close 
And danced a wild teservation two-step 
Until beer cans and disposable diapers 

Spun around us like stars. 
I have surrendered to Leone] Rugama's 
Burning adolescent heat 
And caressed Roque Dalton 
Prom a luxuriance of bedsheets and red wine. 

Once I stayed up all night reading Sherman Alexie, 
Nine months later, I gave birth to twin poems. 

This lust for poetry is by no means heterosexual, 
I devour Nikki Giovanni and Patricia Smith 
Like they are made from the finest chocolate. 
I have been known to steal away for 
An afternoon tryst with Julia de Burgos. 
I wrap Nellie Wong around me like a silk robe. 

Tonight, I have a date 
To share a steamy bath 
With Linda Hogan and Joy Harjo 
And let me tell you 
It's gonna be gooooood. . . . 



36 The Mind's Eye 



Sara Littlecrow-Russell 



Stop Welfare: The Middle Class Is 
Going Broke 

Her shiny, white bumper 
cuts with the angry slash of red — 
"Stop Welfare: The Middle Class Is Going Broke" 
I want to get out of my car 
to teil her that 
my $565 a month for two kids 
ain't got nothing 
on $104.3 billion a year 
called Corporate Subsidies, 
but her face is closed up with hate 
for her work, 
for her graying hair, 
for her day-care bills, 

for my dirty car, 
and my tired clothes. 

I want to talk to her, 
but I know she wifl never understand 
that my $565 a month and two kids 
Is not why her full-time job 

only pays half her bills 
so I sneak out with a marker 
and write "corporate" between 
"stop" and "welfare" 
then quickly drive away. 



The Mind's Eye 37 



Giotto's Arena Chapel 
Frescoes and Religious 
Theater in His Time 

BY CHARLES PARKHURST 

Many readers are familiar with the gnat narrative frescoes by Giotto in the 
Scrovegni Chapel, on the Arena in Padua, which were consecrated in 1305. To 
promote a developing line of thought about these paintings — that Giotto '$ roots 
lie deep in some theatrical tradition — / delivered a paper at the annual meet- 
ing of the College Art Association in San Francisco in 1989 that provides the 
basis for this article. In recent times, scholars have discussed the narrative se- 
quences of the frescoes with regard to their cyclical organization, literary sources, 
realism and their many dramatic qualities. In this essay, I offer a new look at 
these features. Each has a bearing on my objective, which is to open a discus- 
sion of the relationship between Giotto's frescoes and the staging of religious 
plays in his day. 



Late Medieval Sacred Drama 

To understand Giotto's narrative cycles at the Arena Chapel, we 
must know more than we do at present about sacred theatrical repre- 
sentations in the late Middle Ages. Hundreds of such plays are extant 
from Giotto's time. The earliest plays we have are liturgical dramas, 
performed around the altar in churches of the tenth century, among 
them a simple version of the Easter play in a manuscript from St, Gall, 
with a text that is not liturgical but consists of biblical paraphrase, 
written as embellishments prefacing the Easter liturgy. This play was 
depicted by a miniaturist of the same period in another St. Gall manu- 

38 The Mind's Eye 



Charles Parkhursi 



script, which shows that the tradition of illustrating liturgical plays, 
and possibly depicting them without text, may have been established 
by about 950. 

Subsequently, plays were written for other feasts. Later these sa- 
cred representations moved out of the church, into the squares and 
public courtyards of towns, and increasingly were written in the ver- 
nacular. Most distinctive in the development of sacred theater is the 
tendency of playwrights to link individual plays from the church cal- 
endar to form cycles. Also, there emerges a marked preference for 
plays composed on a more ample scale, with notable advance in imagi- 
native elaboration and, consequently, considerable increase in length. 

From northeastern Italy come the most famous historical refer- 
ences to play cycles. These are from the Cronaca Friulitmtt, written by 
canon Giuliano da Cividale in the 14th century. The Friuli is the land 
at the head of the Adriatic, between Padua and Cividale, an autono- 
mous commercial city on the road northward from the sea to the Ger- 
manic lands. This city was the chosen residence of the patriarch of 
Aquilea, whose jurisdiction at certain times included Padua. More- 
over, Cividale was called "Civitas Austriae," and was also the residence 
of the patriarch of Austria. 

There are two entries under the dates 1298 and 1 300 in Giuliano's 
chronicle that confirm that cyclic theater in northeast Italy had reached 
something like its full dimensions by about 1300. 1 translate the sec- 
ond, which is similar to but longer than the first: 

In the year of our Lord 1303 there was performed by the 
clergy, or by the lay chapter of the city, a play, or rather plays, 
as recorded below; in the lirst place a play about the creation 
of our first parents; next about the Annunciation to the Blessed 
Virgin; about the Nativity with many circumstances; and about 
the Passion and Resurrection; the Ascension and the Advent 
of the Holy Spirit; and about the anti-Christ and others; and 
finally about the coming of Christ to the Judgment. And the 
aforesaid plays were performed solemnly in the courtyard of 
my Lord the Patriarch at the Feast of Pentecost and the two 
days following, this being the 15th of May. . . . 



The Mind's Eye 39 



Charles Parkhurst 



Stagecraft and Staging in Late Medieval Religious Theater 

As Hardison wrote, in ihc late Middle Ages, good religious drama 
was a felt experience, like good drama elsewhere; but it also was a 
source of instruction for the layman, intensified by explicitly mimetic 
acting, in real settings and in real time. Medieval Sacre Rappresentazioni, 
as they were known, sought reality through illusion. Actors were re- 
quired "by instruction" to have a physical resemblance to persons they 
represented, and to express themselves in fitting dialogue, reinforced 
through posture, gesture, action, vocal inflection, costume and makeup. 
In short, those who played roles had to strive for convincing, and con- 
sistent, characterization. Anachronism was another form of verisimili- 
tude in medieval drama, for events and settings were often updated, 
and the playwright used his experience as a guide when historical 
improvisation was necessary. 

From theater archives we learn that play production in the late 
Middle Ages included arranging lor the play, finding the text, organiz- 
ing the performance, costuming, selecting the stage crew, providing 
for the audience and, perhaps most important, appointing the direc- 
tor, the musicians and the painter. These documents also reveal sub- 
sequent requirements; sets, machinery, special effects, movement of 
actors, crowd effects, mime and gesture, accounting income and ex- 
pense, storage and repair for the next year's performance, selling off 
and cleaning up. 

Stagecraft and Staging in Giotto 

Staging by Giotto in his Arena Chapel frescoes can have been no 
less complicated. He sets each of his two cycles — "Life of Mary: Her 
Parents and Her Baby" and "Life of Christ: His Mission, Passion and 
Death" — with a separate group of modular stage properties that is used 
only within its proper cycle. The number of scenes presented on any 
set varies, increasing in number in the latter part of the Christ cycle. 
The "stage" itself, with drab dark-brownish floor (when visible) and 
blue backdrop, is constant. 

For the 19 scenes of the Mary cycle' there are but six sets: 
Set 1. Five scenes with variable rocky terrain as in The Flight into 
Egypt show iow gray rocks that can be walked or climbed upon, but 
background mountains are never invaded. A prop may be used to 
identify further the nature of the landscape, such as the sheepfold in 

40 The Mind's Eye 



Charles Parkhurst 



Joachim's Return to His Flock and in Joachim's Vision (fig. 1), and the 
tallest peaks are moved about from scene to scene. 

Set 2 . Anna's cubic one-room house, with a curtained bedroom, a 
porch and upper deck with staircase, appears twice, first in her Annun- 
ciation (fig. 2). It is frontal, but with the front wall removed and the 
side walls squashed on one diagonal perhaps to fit the stage and, at 
the same time, to conceal the angel until its appearance at the win- 
dow. This house is used again in The Birth of Mary, four scenes later. 

Set 3. A post-and-lintel shed seen in The Nativity with Shepherds is 
held over for The Adoration of the Magi, with an accurate image of Halley 's 
comet seen against the blue backdrop. (Giotto very likely witnessed 
the passage of this comet over northern Italy in 1302.) 

Set 4. An exedra with an altar and two side chapels is employed in 
four scenes: The Presentation of the Rods by Mary's Suitors (fig. 3), fol- 
lowed by The Suitors Watching the Rods, and then The Betrothal of the 
Virgin. It is brought back for the final childhood of Jesus scene, Jesus 
Disputing with the Elders. 

Set 5. A spectacular set for The Rejection of Joachim's Offering (fig. 4) 
initiates this "Life of Mary" cycle. (To this very day, an audience en- 
joys applauding a designer's opening set.) It offers a rich sacred enclo- 
sure, in the much earlier Roman tradition of monks' choirs, assorted 
marbleized panels on a low platform, within which is a clothed altar 
and a chest beneath an arched tabernacle with spiral supports and a 
pyramidal top. Beyond is a marbleized ambo supported on colonnettes 
with a staircase, the two flights of which take a turn after about six 
steps up. At the right, Joachim, his offering spurned, is about to he 
shoved rudely onto the drab floor of an empty stage. 

This set reappears in The Presentation of Mary with a change that is 
deceptively simple: It is reassembled in the same conformation but 
rotated 90 degrees on the stage so that its nether side is toward you; 
the ambo. with its dogleg flight of steps, is thereby brought to the 
front and its topmost platform swung broadside. In addition, the set is 
now elevated on a higher styloba te of marbleized panels with the flight 
of steps required for this scene. 

There is yet a third use of this set in The Presentation of the Child, 
wherein only the altar and tabernacle are returned to the stage, this 
time on a low socle, set at still another angle relative to the audience. 

Thus, in the Mary cycle, there are but five basic sets for IS scenes. 

The Mind's Eye A\ 



Charles Parkhurst 




Figure L: Giotto, Joachim's Vision, c. 13 02-0 5 




fit i mm | 

Figure 2: Giotto, The Annunciation to Anna, c.l 302-05 



42 The MindS Eye 



Charles Parkhurst 




Figure 3: Giotto, The Presentation of the Rods: by Mary's Suitors, c. 1 302-05 




Figure 4 : Giotto, The Rejection of Joachim 's Offering, c. 1 302-0 5 



The Mind's Eye & 



Charles Parkhurst 



plus one unique set, which I will discuss below. As to cast, this cycle 
has six principals, six supporting players, five angels, for a cast of 17, 
plus ten extras and about 24 walk-on animals and two doves. (I will 
not analyze the Christ cycle, where the same principles apply, but will 
refer later to one or two scenes.) 

The unique sixth set just referred to is for Joachim and Anna at the 
Golden Gate of Jerusalem (fig. 5), which belongs to this cycle because of 
the presence of the parents ol Mary. To further the reader's under- 
standing of Giotto's stagecraft, I introduce my own stage model for 
this play, in which I visualize an approximation of Giotto's Golden 
Gate scenery as it would be viewed from a spectator's position and 
proportionally framed as in Giotto's frescoes (fig. 6). The model con- 
sists of three parts: a towered gate, a painted flat visible through the 
gate to suggest the city within and a side rail for an arching bridge. 
Giotto's prototype for the Golden Gate, I believe, is L'Arco Etrusco in 
Perugia (fig. 7). This ancient northern gate has been part of the defen- 
sive wall of Perugia since at least 300 b.c.e. and many times repaired 
and restored. Today it still spans via Flaminia, the ancient cross-coun- 
try highway leading from the Forum in Rome, up the Tiber Valley to 
Perugia and beyond, northward. Its appearance in Giotto's frescoes 
suggests that the inspiration he took from his own ambience included 
architecture as well as theater, I must also call your attention to a 
telling detail in the staging: Anna is standing not on the rising bridge, 
as you are meant to suppose, but on the brown plane of the stage, for 
her feet are at the same level as Joachim's. 

A conspicuous feature in nine scenes of the Mary cycle is a pulpit 
or other accessible high place, which, though depicted by Giotto, is 
not utilized by him in a scene. Why is it there? The only explanation I 
can offer is that these high places in a setting had a use in the play, but 
not at the dramatic moment Giotto depicted them. For example, the 
great opening scene of the Mary cycle (fig. 4) has an arabo, an acces- 
sible high place with steps. Now, every sacred representation opens 
with a salutation by an angel who comes on stage annunziare lafesta, 
and to explain in song what the audience is about to see. Explicable 
only as a theatrical element, the ambo's appearance in Giotto's fres- 
coes confirms that he was deeply informed by those traditions. 

I deduce the following about Giotto's stage, as it would be without 
sets. First, it has a dark brown or sometimes dingy terre verte floor, 

44 The Mind's Eye 



Charles Parkhurst 



with no material identification. Perhaps it is packed earth or painted 
cloth. Second, it has a blue backdrop or wall, which does not change 
with respect to any attribute or property of blueness. Third, the stage 
dimensions are sufficient to accommodate as many as 21 or 22 actors, 
with props. Fourth, your eye as a spectator is uniformly about mid- 
level of the scene, which is the eye level of the principal actors. This 
also explains the prevailing isocephaly, and permits the conclusion 
that the stage is at ground level. Your position is otherwise not fixed, 
and you are free to move right or left in the nave of the chapel. Last, 
calculating from figure size, I estimate that the area of Giotto's stage is 
about 150 square feet— about 15 feet wide at the front and 10 feet 
deep (see the stage shown from the front [fig. 6], and a rear view as 
well with support scaffolding, platforms and ladder [fig. 8]). 

I call your special attention to three other features in Giotto's fres- 
coes that relate to staging: lighting, special effects and crowd scenes. 
Regarding the first, the lighting suggests daylight, as it would be in 
outdoor theaters on clear days, when performances could be given. 
How do we know this? In the frescoes, as in nature, as has been previ- 
ously suggested by others, light is revealed by color alone: direct light 
by strong color on salient bodies, graded as necessary up or down: 
circumferential and diffused light by subtly grayed hues in the pen- 
umbra. Nothing is obscured by darkness. Moreover, as Paul Hills has 
elucidated, Giotto causes this painted or fictive light to be congruent 
with the real light of the chapel. That is, it either seems to come bright 
and direct from the high west window or is less bright and diffused, 
pooling shadows under simulated overhanging projections in the set- 
tings. This is a large part of Giotto's celebrated naturalism. 

Second, special effects and deus-ex-machina arrangements are 
evident in 1 2 scenes, of which eight include airborne angels. I propose 
that Giotto's theatrical solution was not the then commonplace wires 
or thin ropes worked on windlasses but rather a system of his own 
invention. Close examination of a flying angel (fig. 1) reveals that its 
head and shoulders are depicted as three dimensional, whereas the 
rest of its body and its wings appear flat and to evaporate "into the 
blue.'' My surmise is that this putative angel, supported on a platform 
of the scaffolding behind a special, slitted blue backdrop (fig. S), thrust 
its head, shoulders and arms through a slit next to which its wings 
and tail were either affixed as attachments or painted directly on this 



The Mind s Eye 45 



Charles Parkhurst 




' Charles Parkhursl 




The Mind's Eye 47 



Charles Parkhurst 

special backdrop. This conjecture seems reasonable in view of the cloth 
roll visible around each angel's torso, just under its armpits, where the 
backdrop would cut into its body. Was this Giotto's invention? 

Third, staging of a crowd scene contains other challenges. How on 
earth could Giotto have been led to accept, for The Kiss of Judas in the 
"Life of Christ" cycle, approximately 60 performers on a stage com- 
fortable for 20? The first step toward an explanation of this incongru- 
ity is to count only the visible faces (21 or 22), then compare the other 
(40-some) heads in the background, which are faceless, represented 
only by the tops of black helmets. For the a dual stage play, these massed 
helmets (black because of the corrosion over time of their silver leaf) 
may have been painted on a separate "flat," possibly with small boys 
crouching behind to joggle that flat and to wave spears and cressets 
for increased verisimilitude. Giotto thus took his cues front the real 
theater, problems and all. In any event, the prototype for Giotto's fres- 
coed stages had to be a real, working stage. 

Relating Some Extant Plays to Giotto's Pictures 

Now let us move away from these intriguing inferences and de- 
ductions and turn to extant plays of the time. It Giotto took his inspi- 
ration from the theater, he got at least hints of its staging and sources 
along with the texts of its plays. 2 

Of several plays I have found thus far that are related, the closest 
is that of the Annunciation. But it could hardly be otherwise, for the 
play of the Annunciation was performed annually from about 1278. 
out of doors, in the arena, but not inside the chapel. The double stage 
set for the play, depicted by Giotto on the east wall of the Arena Chapel 
(fig. 9 shows only The Virgin Annunciate), I suggest, depicts or reflects a 
two-part set of portable stages or "chairs" carried on long poles, the 
documented costs for all of which were discovered by R. Zanocco in 
1937 in the archives of the Cathedral of Padua, as "expenses incurred 
by the sacristy after due discussion ... in the year 1305 . . . Wednes- 
day, the 24th of March" (see Stubblebine 1969). These portable stages, 
and their actors, were carried in a great procession from the Cathedral 
to the Arena for the performance of the play of the Annunciation. 

For this play, there are extant 14th-century manuscripts from 
Padua, which describe the occasion in detail and almost certainly record 
the play as performed at the consecration of the Scrovegni Chapel, on 



The Mind's Eye 



Charles Parkhurst 




Figure 9: Giotto, The Virgin Annunciate, c. 1302-05 




Figure 1 0: Giotto, The Guard Set by Pilate and the Noli Me Tangere, 
c. 1302-05 



The Mind's Eye 49 



Charles Parkhurst 



March 25, 1 305. These provide the dialogue, the casting, set, curtain- 
ing, gestures and movements, descent of the dove, and so on, which 
are generally similar to what we have in the frescoes. 

I invite your attention to two other plays of Giotto's time, one with 
a general and the other a specific application to our two narrative cycles. 
The first of these is an extant text of a passion play in the archives of the 
cathedral in Cividale. This play includes the lamentation of Mary and 
others at the Crucifixion, On the Cividale manuscript (fig. 11), players 
are indicated in the right margin, opposite their lines. Amid the square 
notes on the four-line music staff, one can even detect the rubrics of 
stage directions. Below the staff is written the dialogue 



j# i'Ylltli tf^TlI* ' 1 - .. >».- m — i ■ - ■ --fr i i i - i jwf ■ 



vfo\ tDtafilnsarriAjUrernn. -colts pi^toloj, K30 mm. 
qaave ttlv^re petite? itajritt lis aitt nwtir rw ar>:i' (5 



Figure 11: From Liturgical Drama of the Middle Ages, I860, by E. de 
Cousscmakcr 

I translate here the first five stage directions pertaining to the 
Magdalen's acting. You will note the care with which the rhetoric is 
supported by realistic gestures and postures, which could scarcely be 
more specific. Many details suggest a relationship with Giotto's Cruci- 
fixion and Lamentation. 

(Here she turns to the men with arms extended.) 
(Here she turns to the women. ) 
(Here she beats her breast.) 

50 The Mind's Eye 



Charles Parkhurst 



(Here she raises her hands.) 

(Here, inclining her head, she seats herself at the feet of Christ.) 

My second analogy is afforded by Giotto's Easter drama. Here, in 
one set he selects and combines moments from three contemporary 
plays: The Visit of Mary to the Tomb, the episode of The Guard Set by Pilate 
and the Noli Me Tangere (fig. 10). It is particularly significant that in the 
guard episode, five soldiers lie unconscious before the empty tomb, 
whereas usually but three are represented, and rarely two or four. 
Five guards appear only in plays written in Germany. The earliest 
known passion play text of this scene is of the late 1 3th century and 
comes from the monastery at Ottobeuren, Bavaria. Tellingly, it includes 
a conversation in Latin amung five soldiers at the tomb. I believe Giotto's 
painting is unique in this last detail. 

How could a German play reach Giotto? Tt may have come down 
the "Friuli corridor," from the German lands to Cividale, and thence 
to Padua or elsewhere, as I suggested above. Bear in mind that Giotto 
certainly was an informed man, cited in his liletime by his home city, 
Florence, for scientia et doctrina. He also might have had connections 
with Ottoman Germany, perhaps through the considerable influx of 
Germans into northern Italy in his day, including German stained- 
glass- window makers at the new church of St. Francis, in Assisi. 

Envoi 

There is an intensity in Giotto that does not come entirely from 
religion, nor from the pictorial tradition. I believe it comes from the 
theater. As I have pointed out, there exist many archival documents 
concerning stagecraft and staging in the 13th and 14th centuries, and 
I wish to suggest that the Arena Chapel frescoes should be listed promi- 
nently among them. I believe that Giotto's previous education and/or 
actual experience must have included the theater. This completes 
Giotto's image as an artist and that of his spectators as participants, 
and both as lovers of religious drama. 

The Sucre Rappresentazioni were entertainment in public life, but 
also religious instruction. Giotto, like a stellar professor who inspires 
students to be better than he, does not debase the powers of the Gos- 
pel. But in his frescoes, he provides snatches of diverse conversations 
from an artistic world of religious enchantment, the theater, giving 
these frescoes a mysterious, and silent, power. 



The Mind's Eye 51 



Charles Parkhursi 



But how silent were they? With this question I come to ray final 
point about Giotto and the religious stage, on the importance of dia- 
logue, for religious plays in his limes were full of sound, even noisy 
dialogue, explication, music and singing, chanting and sound effects, 
These plays were, indeed, often a sort of proto-operatic production, 
sung in an appropriate musical mode of the day, in words of rhyming 
poetry, beautiful poetry. Did Giotto recognize this sound and music in 
his frescoes? Yes, he did: Trumpets are blown, a horn is sounded, a 
viol bowed, many mouths are singing or wailing, hands are raised in 
speaking gestures throughout — and consider the animals! 

Notes 

' The 19 scenes include thel2 frescoes dealing with the life of Mary 
and then seven more frescoes (including the two Annunciation fres- 
coes) that invulve Mary but overlap with the life of Christ, up to the 
scene of the child in the temple. 

2 As the reader may know, it has been proposed that Giotto's first job, 
apart from sheepherding on his father's farm, was to work in Umbria 
as an assistant-under-instruction to the Florentine artist Cimabue, head 
painter at that time in the basilica of St, Francis under construction at 
Assisi. Cimabue was drawing and painting a border of repeated 
modillions just beneath the windows of the apse and transepts at that 
time. Professor Samuel Edgerton has proposed that the assignment 
given by Cimabue to his new teenage helper was to follow his lead 
and continue this roodiliion molding down each side of the nave and 
across the front wall above the doors at the main entrance to the nave, 
drawing first, then painting in a finished manner something like 400 
identical modillions from a high scaffolding. Edgerton tells the whole 
story about the teenager's skill in painting these modillions in terms of 
a new perspective (up to then not previously conceived by any artist, 
let alone by one who is your "boss"). This included the invention and 
the added figuring of complicated perspectives required, which 
Cimabue himself was clearly unaware of. In the end, the boy Giotto 
was correcting and modifying the ways of his old-fashioned and out- 
dated mentor. As far as we know, Cimabue was not offended, and 
maybe pleased. 

Perhaps because of his inborn, and now displayed, theatrical tal- 



52 The Mind's Eye 



Charles Parkhurst 



ems for perspective while at Assisi, Giotto is likely to have connected 
with a lay confraternity in nearby Perugia, where he would have been 
found most useful with respect to theater performances being staged 
by the Confraternity of St. Andrew, one of the earliest producers (per- 
haps before 1 300) of religious plays in that city. The St. Andrew group 
compiled a book of lauds (read "hymnbook"), and also a playbook (of 
well over 100 plays), both of which are extant only in later copies. 

Annotated Bibliography 

Barr, Cyrilla. The Monophonic Lauda and the Lay Religious Confraternities 
of Tuscany and Umbria in the Late Middle Ages, Early Drama, Art 
and Music Monograph Series 10. Kalamazoo: Medieval Insti- 
tute Publications, Western Michigan U, 1988. 
A rich source for both musical and nonmusical information. 

Cole, Bruce. Giotto and Florentine Painting, 1280-1375. New York: Harper, 
1976. 

The author justifies his reputation as an excellent teacher. Rec- 
ommended for its thorough and lucid presentation without 
belaboring the problems. Well thought out and consistently 
articulate. 

Edgerton, Samuel Y. , Jr. The Heritage of Giotto 's Geometry: Art and Science 
on the Eve of the Scientific Revolution. Ithaca: Cornell UP, 1 991. 
By one of our most gifted and readable scholars in the high- 
speed field that joins science, art and history, who has a gift for 
unknotting complicated subjects and displaying them as a neck- 
lace of new ideas, sparkling with verve. A must-read section on 
the young Giotto's first job at Assisi. 

Eisenbichler, Konrad, ed. Crossing the Boundaries: Christian Piety and the 
A rts in Italian Medieval and Renaissance Confraternities. Early Drama, 
Art and Music Monograph Series 15. Kalamazoo: Medieval In- 
stitute Publications, Western Michigan U, 1991. 
Experts discuss a variety of subjects pertaining to this period. 

Hardison, O.B., Jr. Christian Rite and Christian Drama in the Middle Ages: 
Essays in the Origin and Early History of Modern Drama. Baltimore: 
Johns Hopkins, 1965. 

These essays by the late director of the Folger Library, Wash- 
ington, D.C., are brought together in a handy volume that is 
authoritative and a pleasure to read. 



The Mind's Eye 53 



Charles Parkhunt 

Hills, Paul. The Light of Early Italian Painting. New Haven: Yale UP, 1987, 
A rare topic, treated with skill and deep knowledge. Chapters 
2, 3 and 4 pertain to Giotto's Arena Chapel frescoes and those 
artists who proceeded or followed him, to light and color, and 
to the color scientists of the day. Abundantly illustrated and 
footnoted. 

Stubblebine, James H., ed. Giotto: the Arena Chapel Frescoes. New York: 
Norton, 1969. 

This contribution to the Norton Critical Studies in Art History 
provides excellent coverage of the frescoes in an introductory 
essay, with the addition of background material and criticism 
from outstanding authors, much of which is hard to come by. 
Young, Carl. The Drama of the Medieval Church. 2 vols. Oxford: Clarendon, 
1933. 

Although almost 70 years old, this text is still very useful, be- 
cause it covers the relevant dramatic liturgy of the Church of 
Rome and goes into detail of plays, among many others, associ- 
ated with the Resurrection, the Passion, the Nativity and the 
Virgin Mary. 



54 The Mind's Eye 



Book Review 



Water out of a 
Woodland Spring 

John Fowlesand Nature, "Fourteen Perspectives on Landscape' 
Edited by James R. Aubrey 
Associated University Presses, 1999 

BY TONY GENGARELLY 



The breakwater at Lyme-Regis, known as the Cobb, describes a 
beautiful arc as it curves into the rough seas of the English Chan- 
nel off the southern coast of England. If we close our eyes, per- 
haps we can see — balanced on the tip of this projection into the wild 
ocean, seemingly united with the power of the natural world — the 
figure of a woman, Sarah Woodruff, the haunting heroine of John 
Fowles's best-known work, his 1969 novel The French Lieutenant's 
Woman. Sarah, one of many connections to wild nature in the literary 
work of Fowles, is drawn out of the author's elemental relationship to 
the natural world. This connection is variously explored by several 
scholar- writers in a 1999 volume of essays, John Fowles and Nature, 
edited by James Aubrey. The authors' viewpoints cover a variety of 
disciplines, from geology tn ecofeminism. With its captioned photo- 
graphs that add greatly to the appreciation of the written text, this 
book is a must read fur anyone looking fur well-informed and beauti- 
fully articulated literary criticism. 

Thanks to the lucid quality of the prose — expertly organized and 
edited by Aubrey — one does not have to be a devotee of John Fowles 
to appreciate the author's search, and that of his fictional characters, 



The Mind's Eye 55 



Tony Gengardly 



for self-actualization through the experience nf wild nature. This vol- 
ume reaches through Fowles's lung and productive career to locate 
him in a variety of settings, from Greek islands to the pueblo ruins of 
the American Southwest- Always preferring the unique, remote places, 
Fowles turns a number of traditional associations upside down as he 
embraces the untamed islands of nature. For Fowles, man is an island 
and the moments of personal encounter with the wild, when people 
are most isolated from the familiar hold of civilized living, are those of 
growth toward personal freedom as well as integration with the larger 
universe (Aubrey 27-30). Wilderness, then, is the central feature of 
the natural wurld, the place beyond the mythical gardens — Eden 
or Arcadia — from which we need to be expelled to begin the process 
of awareness and human development. Fowles, similar to Loren Bisley, 
has a scientist's knowledge of nature without the need to classify and 
organize it for utilitarian purpose. Nature simply is and as such offers 
a life resource that resonates within us all. Fowles's home, Belmont, 
near the Undercliff above the seacoast village of Lyme, not only nudges 
the location of his best-known novel but features as well a "wild gar- 
den," or "English Garden of Eden." It is the unkempt portions of the 
natural world, therefore, that provide Fowles with many of his liter- 
ary themes. The more prominent of these — evolutionary progression, 
the "inverted pastoral" and the Green Man myth — are explored at 
some length by the authors. 

For Fowles, landscape suggests earth history and that, in turn, 
implies evolution. Just beneath the surface of the planet is the discov- 
ery of geological or "deep" time to remind us of "the relative insignifi- 
cance of the lives of individuals against the sweep of time and history" 
(Fadian 1 60). This broad view introduces not only a sense of orderly 
progression but the inevitability of change and the randomness of 
natural selection. Fowles sees evolution as an existential reality — some- 
thing that impacts on the here and now — rather than abstract theory, 
It is through the recognition of this reality that people have the chance 
to adapt, to attain self-actualization by shedding the social conven- 
tions that present an illusion of control. The principal male protagu- 
nist in The French Lieutenant's Woman, Charles Smithson, is an amateur 
geologist, something the leisure time of his privileged status makes 
possible. He is also an avid student of the work of Charles Darwin, He 
is, however, unaware that his radical ideas, which challenge the pre- 

56 The Mind's Eye 



Tony Gengarelty 



cepts of religion, may also apply to the inevitable demise of his own 
social class. Charles's experiences with the wild nature of the Undercliff, 
where he occasionally wanders while searching for fossils embedded 
in the cliff rocks above and below, unravel his neat theories and con- 
front him with the elemental forces thai are moving beneath his com- 
fortable universe. Fowles casts Smithson in the role of quester, the 
male hero who undergoes transformation through an encounter — in 
this case, with wild nature. Through this experience, Charles comes to 
recognize those forces that will carry his destiny to places where he no 
longer sits as the apogee of evolutionary "progress." Fowles's deter- 
minism, though, is balanced with the idea that reality, once acknowl- 
edged, can liberate the individual to make adjustments, quality choices 
that lead not only to self- discovery but to a new level of adaptability 
and survival. 

Fowles uses another theme, the "inverted pastoral," to punctuate 
the role of wild nature in the personal evolution of his protagonists. 
The traditional Edenic or Arcadian pastoral is a location of peace and 
tranquility that lies outside time, a retreat that provides a "vision of 
the ideal to take back to civilization" {Beatty 170). However, Fowles's 
characters need to fall from their imaginary Edens into the wilderness 
of experience, to confront the elemental forces in wild nature that are 
resonant in themselves: "Fowles sets up a pastoral frame of reference 
and simultaneously undercuts it" (Beatty 171). It is as if the author 
had in mind the 19th-century landscape paintings of Constable and 
Turner, the former presenting the rural tranquility of a bucolic ideal, 
the latter introducing the rhetorical sublime with its wild and elemen- 
tal forces. In The French Lieutenant's Woman, Fowles uses a variety of 
images and experiences to punctuate his characters' "fall": the noisy 
call of the wren that defies classification and represents the parity of 
all existence; the presence of an Eve, an anima spirit, in the person of 
Sarah Woodruff, who initiates Charles into the subversive elements of 
wilderness: "With Sarah in the Undercliff, Charles steps out [of his 
comfortable, male-dominated world] into a wild, primeval place, a 
place offering the potential for direct, unsublimated experience — sen- 
sual, sexual, emotional, physical" (Ross 1SS). Sarah is inextricably 
connected to the wild places she frequents, "the physical correlatives 
of her psychic landscape and emotional weather" (Ross 187). This as- 
sociation is made beautifully apparent as Fowles describes Sarah's sor- 



The Mind's Eye 57 



Tony Gengarelly 



row "welling out of her tragic face 'as purely, naturally and unstoppably 
as water out of a woodland spring'" (Ross 186). So the pastoral myth, 
with its spiritual and transcendental overtones, is recast by Fowles as a 
static refuge that limits freedom and personal evolution. Aware of his 
own century's reaction against the taming of the wild, Fowles invites 
the reader to participate in a liberating rite of nature: "Thus Fowles's 
true Eden ... is predicated on the evolutionary process; paradoxically, it 
necessitates its own loss, a 'fortunate fall' into the recognition of reality, 
undiluted and unmediated by a pastoral myth that may inhibit the 
individual's personal growth" (Beatty 178), 

The nature of nature for Fowles is found in the Wild, represented 
by the mythical Green Man. In The Tree (1983), Fowles describes the 
Green or "Wild" Man as a numinous source of creativity and self- 
expression, something that needs to be protected from a worfd that 
would reduce it to a mere classifiable thing. Tracing the evolution of 
the Green Man to the English story of Robin Hood, an outlaw taking 
refuge in the Green Wood, Fowles expands on the need for civilized 
people to embrace wild places in order to nurture their own creative 
potential: "Some such process of retreat from the normal world ... is 
inherent in any act of artistic creation. . . . And a part of that retreat 
must always be into a 'wild,' or ordinarily repressed and socially hid- 
den self. , . . The return to the green chaos, the deep forest and refuge 
of the unconscious" (Fowles 75-76). Western civilization's fear of the 
unknown external world and the subconscious self, often represented 
by natural wilderness, has inspired the desire to clear the forests, to 
use them for lumber, to expose the refuge of the Green Man. Fowles 
speaks out against this fear-driven desire to civilize, objectify and con- 
fine the free spirit of the woods inherent in all of us. 

In Fowles's autobiographical novel, Daniel Martin (1977), the quest- 
ing hero searches out those natural places where personal transfor- 
mation is possible: "These are the settings that evoke the majesty, 
mystery, and power of Nature; that provoke epiphany and whole vi- 
sion . . . that challenge conventional notions of language and time and 
enable profound transformations of feeling and perception" (Olshen 
108). In Fowles's 1974 novella. The Ebony Tower, his artist-hero, Henry 
Breasley, undertakes a rearguard action against abstract art that repre- 
sents "the turning away from nature and the physical world on the 
one hand; and the fear of the body, desire, and appetite on the other" 

58 The Mind's Eye 



Tony Gengarelfy 



(Olshen 109). Paradoxically, early modem art used abstraction to em- 
brace the primitive, to free the artist from civilized constraints. 
Gauguin's refuge in Brittany and the South Sea islands, the Worpswede 
movement in German art and the Fauves ur "wild beasts" sought to 
tap the "green chaos" found in traditional, indigenous societies as well 
as the human subconscious. 

Fowles found his own wilderness refuge in Belmont, near the 
Undercliff, which became for him in The French Lieutenant's Woman the 
central place where those who were exiled to or from the regenerative 
powers of the wild might locate. 1 It is, of course, Sarah Woodruff who 
is identified with wild places, with the tip of the Cobb and the Undercliff 
where she wanders. Having been banished to these natural places, as a 
woman and social outcast, Sarah embraces wild nature to achieve her 
freedom. Charles Smithson, as a representative of the male-dominated 
social order, is accordingly exiled from the wild and needs a "fortunate 
fall" into the "green world" to begin the process of discovering the 
larger realities that condition his lite. So, ultimately, one learns from 
these essays in this very perceptive volume that "the world of nature 
. . . rather than a marginal location ... is instead a central place . . . 
resonant with the green chaos in all of us" (Ross 192). 



1 Traditionally, the Undercliff was a secret gathering place for Puritan dissenters in the 
1 7th century, who congregated at whitechapel Rock, a totemlike projection in a thicket 
ot Undercliff woods. Here the wilderness protected and fostered the Puritan need tor 
religious freedom. Ironically, once the Puritans established their "City on the Hill" in 
Massachusetts, they began to fear the wilderness as a refuge for those who would un- 
dermine their holy mission. The forests became the abode of witches and "red men," 
Quakers and freedom lovers, who were perceived as agents of the Devil by God's "elect. " 



The Mind's Eye 59 



Tony Gengardly 

Works Cited 

Aubrey, James R, "Introduction." John Fowles and Nature, "Fourteen 
Perspectives on Landscape." Ed. James R. Aubrey. London: As- 
sociated UP, 1999. 

Barnum, Carol M. "The Nature of John Fowles." John Fowles and Nature, 

Bawden, Liz-Anne, Kevin Padian and Hugh S. Torrens. "The Undercliff 
of John Fowles's The French Lieutenant's Woman: A Note on Ge- 
ology and Geography." John Fowles and Nature. 

Beany, Patricia V. "The Undercliff as Inverted Pastoral: The Fowlesian 
Felix Culpa in The French Lieutenants Woman." John Fowles and 
Nature. 

Fowles, John. The Tree. New York: Ecco, f 983. 

Olshen, Barry N. "The Archetype of the Green Man in the Writings of 

John Fowles." John Fowles and Nature. 
Padian, Kevin. "Deep Time, Evolutionary Legacy, and the Darwinian 

Landscape in John Fowles's The French Lieutenant's Woman." John 

Fowles and Nature. 
Ross, Suzanne. '"Water out of a Woodland Spring': Sarah Woodruff 

and Nature in The French Lieutenant's Woman." John Fowles and 

Nature. 



60 The Mind's Eye 



Book Review 



Intellectual Fads 



Thinks ... by David Lodge 
Viking Penguin, 2001 

BY MEERA TAMAYA 



David Lodge is one of those rare protean and prolific writers 
who practice their craft successfully in multiple genres: nov- 
els, plays and criticism. For years he was also an academic, 
affiliated with the University of Birmingham. However, he is best 
known for his hugely entertaining novels satirizing the theoretkat 
battles lought, often pompously and always humorlessly, in the groves 
of academe, Changing Places, Small World and Nice Work, for example, 
pillory well-known literary theorists and the hostilities between town 
and gown. 

Since Lodge's antennae are always aquiver to register the slightest 
shifts in the winds of intellectual fashions, it is not surprising that his 
latest novel. Thinks . . . , takes on the "problem" of consciousness, the 
current hot topic debated by neuroscientists, psychiatrists, philoso- 
phers and linguists. Consciousness — the complex web of thoughts, 
feelings, memories of the past and intimations of the future that consti- 
tutes our interior life — is perceived as a "problem" by the intelligentsia 
partly because the computer's increasing usurpation of the brain's func- 
tions has brought into question what was traditionally considered a 
uniquely human attribute. All of us remember the defeat of Garry 

The Mind's Eye b\ 



Meera Tamaya 



Kasparov, the chess master, by the IBM computer Deep Blue. As Ar- 
tificial Intelligence, or A.I., becomes a possibility, the mechanical rep- 
lication of consciousness looms in the not too distant future. 

Or so believes the eponymous Ralph Messenger (a harbinger of 
the future?). Professor anci Director of the Holt Belling Center for 
Cognitive Science at the fictional University of Gioucester. Thinks . . 
begins with the recording of Messenger's most private thoughts and 
feelings as he dictates into his Olympus Pearlcorder, in his own words, 
"The object of this exercise being to try to describe the structure of, or 
from which one might infer the structure of . . . thought.' Messenger's 
consciousness is driven by twin goals: vigorous sell-promotion and 
the satisfaction of his libidinal urges. When he is not planning his ca- 
reer advancement, he is savoring his past and plotting his future sexual 
exploits. He is not above hiding the recorder under the pillow of his 
latest sexual partner without her knowledge. Messenger, of course, 
has no truck with old-fashioned ideas of God or the existence of a 
soul. Indeed, he thinks consciousness is a synchronized affect of vari- 
ous brain functions and, as such, will be replicated by a computer in 
the near future. 

Messenger's biological reductionism is anathema to the woman 
he pursues and, finally, wrangles into bed: Helen Reed, a visiting pro- 
fessor of creative writing. Helen, a recent widow and a successful nov- 
elist, is a lapsed Catholic who is not yet ready to give up entirely on 
comforting notions of God and the immortality of the soul. Also as a 
writer of old-fashioned realistic novels, she fights a rearguard action 
aga i nst postmodern, poststructuralist deconstru ction of th e subj ect and 
its attendant notions of individual, autonomous identity. Messenger 
and Reed represent what C. P. Snow in a 1959 lecture called the Two 
Cultures: the Sciences and the Humanities, which, according to Snow, 
exist in mutually uncomprehending opposition. Messenger's court- 
ship of Helen (under the nose of his rich American wife, who is also 
having her own adulterous affair) is conducted largely like an intellec- 
tual seduction. He has to break down her distaste for a liaison with a 
married man as well as her steadfast loyalty to passe ideas of soul, self, 
subject, identity, etc. 

Their affair follows its banal, very predictable course and Lodge, 
who has written extensively on the novel, cannily has Helen justify- 
ing adultery as a plot device: "There's not a great deal of narrative 

62 The Mind's Eye 



Meera Tamaya 



mileage in the stable monogamous marriage." Besides Reed and 
Messenger, almost everyone in the novel is playing musical beds, but 
the extramarital lovers come across as marionettes, doing the bidding of 
the novelist to provide some sexual ballast to all the intellectual hot air. 

Messenger and Helen's intellectual conflict provides Lodge with a 
narrative strategy for making complex ideas about consciousness in- 
telligible to the general reader. Playing the naif, Helen questions Mes- 
senger, enabling him to expound and explain recent developments in 
cognitive studies, beginning with Descartes' formulation "Cogito, ergo 
sum ": I think, therefore, I am, His dictations into the Pearkorder and 
pages from her diary provide alternating points of view, intermixed 
with the third-person authorial overview. 

As in Small World, the denouement of Thinks . . . occurs at an inter- 
national conference on Consciousness Studies known as Con-Con to 
its habitues. Messenger enlists Reed to give the final lecture, 'The Last 
Word," and she points out that "consciousness . . , is to modern sci- 
ence what the philosopher's stone was to alchemy; the ultimate prize 
in the quest for knowledge." As an unreconstructed humanist, she 
goes on to proclaim that "literature is a written record of human con- 
sciousness." In support of her heartfelt defense of a nonscientiiic view, 
she cites Andrew Marvell's poem "The Garden," in which "We can see 
the fruit, we taste it and smell it with what has been called the thrill of 
recognition, and yet it is not there, it is the virtual reality of the fruit." 

Reed sounds like a stand-in for Lodge, the novelist, but the irony 
is that Thinks . . . fails to convey the "virtual reality" of a fictional world. 
That the novel is merely a vehicle for an intellectual debate is all too 
apparent, and, consequently, the characters are not fully fleshed and 
engaging. The wit and inventive exuberance of his earlier novels are 
also missing, as if the subject of consciousness is too serious to be trifled 
with. Indeed, the novel could have been more accurately titled A Guide 
to Recent Developments in Cognitive Studies — it works better as a guide 
than as a novel. 



The Mind's Eye 63 



Contributors 



Tony Gengarelly leaches an history and museum studies at Massachusetts 
College of Liberal Arts. He has written several articles and books, including a 
1 989 catalog. The Prendergasts and the Arts and Crafts Movement, and a 1 996 mono- 
graph. Distinguished Dissenters and Opposition to the 1919-1920 Red Scare. His 
essay on Frederick Stroth mann's poster "Beat Back the Hun with Liberty Bonds" 
appears in American Dreams: American An to 1950 in the Williams College Museum 
of Art. He has also contributed an entry, "Poster Art." to The Guide to United 
States Popular Culture. 

Sara Littlecrow-Russell is Metis and lives In Boston, where she attends 
Northeastern Law School. Her poems have appeared in US Latino Review, Red 
Ink, American Indian Quarterly. Femspee, The Massachusetts Review, Flyaway, Hip 
Mama, RaceTraiwr Journal, Survivor and a variety of anthologies, including the 
forthcoming New Rivers Press anthology Sister Nations. Her poem "Ghost Dance" 
appears in All Our Relations: Native Struggles for Land and Life, by Winona LaDukc. 

Joe Mazur is a professor at Marlboro College, where he has taught math- 
ematics since 1 972. For the past 1 5 years, he has been publishing educational, 
interactive multimedia software. Joe is the author of many software packages 
that accompany more than 20 textbooks from five areas of elementary college 
mathematics. He is the author of Explorations in Calculus, a multimedia CD 
package of simulations for first-year calculus. The essay that appears in this 
issue is the first chapter of a book he is currently writing, What I Tell You Three 
Times Is True. 

Charles Parkhurst is an art historian who lives in Amherst. He served as a 
U.S. Naval Reserve combat officer during World War TT, afier which he aided 
the art search-and-rescue efforis of the U.S. Army of Occupation in southern 
Germany. Parkhurst was professor and chair of the Department of Fine Arts 
and director of the Allen Memorial Art Museum of Obcrlin College from 1 949 
to 1962, director of the Baltimore Museum ol Art from 1962 to 1970 and 
assistant director and chief curator of the National Gallery of An from 1971 
until his retirement in 198 J. Since then, he has been acting director of the 
Williams College Museum of Art and of the Williams College Graduate Pro- 
gram in the History of Art and interim director of the Smith College Museum 
of Art. In the spring of 2001, he was lecturer in residence at Massachusetts 
College of Liberal Arts. Parkhurst has published articles and books on mu- 
seum management, art history and the history of color science. 

Meera Tamaya is a professor of English at Massachusetts College of Liberal 
Arts, where she teaches courses on Shakespeare and other distinguished writ- 
ers. She is the author of the book Colonial Detection: H.R.F Keating, as well as 
articles on John Sherwood, Kazuo Ishiguro, Margaret Aiwood. Barbara Pym 
and Shakespeare. Her most recent book is An Interpretation of Hamlet Based on 
Recent Developments in Cognitive Studies. 



64 The Mind's Eye 



Mind's Eye 

Writer's Guidelines 



While emphasizing articles of scholarly merit. The Mind's Eye focuses on a general 
communication of ideas of interest to a libera] arts college. We welcome expository 
essays as well as fiction. We publish twice a year. The deadline for the Fall issue is 
July 15. Deadline for the Spring issue is January 15. 

Submissions should adhere to these guidelines: 

1. Submit unpublished manuscripts both on paper and on disk, using either PC or 
MAC platform word-processing programs. Manuscripts should be typed double 
spaced and printed on one side of the paper only. List your name, address, phone 
number and e-mail address, if available, on the cover sheet, and your name at the 
top of each page. 

2. We will consider simultaneous submissions under the provision that the author 
notify us of this and contact us immediately if the material is accepted elsewhere. 

3. if you wish your manuscript and disk returned, please enclose a return self- 
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we make every attempt to safeguard your manuscript and disk, we cannot be held 
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4. Use MLA or APA style, with in-text references, as appropriate to the content and 
disciplinary approach of your article (see MLA or APA stylebook for guidelines). 

5. While we will consider articles of unspecified length, preference is given to 
articles of fewer than 20 pages. 

6. We reserve the right to edit for clarity and accuracy. 

7. We will consider one-color artwork (e.g., photographs, line drawings, woodcuts). 

8. Payment will be made in contributor's copies. 



Submit your manuscript to: 

The Mind's Eye 
Tony Gengarelly, Managing Editor 

Massachusetts College of Liberal Arts 
375 Church Street 
North Adams, MA 01247 
For queries: agengare@mcla.mass.edu